72180a No.7690 [Last50 Posts]
The virtual quantum computer (VQC) is a grid made of infinite yet constructable sets that follow a known pattern. Like a quantum spreadsheet.
The grid is the superposition. The collapse of that superposition will be two input parameters, d and e which can be calculated easily for all integers, c, where c is the difference of two squares. Its purpose and our goal is to learn and show the TRUTH, one of them being P=NP. Cracking RSA will be a consequence.
When the integers that are the difference of two squares are arranged into the grid and their corresponding properties are shown, a pattern emerges that shows calculation instead of searching is possible.
Glossary
Column
All cells for a given e.
Row
All cells for a given n
The grid is indexed using e, n, and t, where e is the rows, n is the columns, and t is the specific element in the cell.
Entry, record, element
one set of variables that represents one factorization for a number.
an entry = {e:n:d:x:a:b} (e, n, t)
{1:5:12:7:5:29} (1, 5, 4) is a record AKA an element AKA an entry.
ab record, nontrivial factorization, prime record
the element that contains the factorization of c that is not 1*c, hence, nontrivial.
1c record, trivial factorization
the element generated from setting a=1 and b=c
Cell
All entries for a given e,n (not to be confused with an entry itself.)
Genesis cell
e,1
Remainder Tree
The remainder tree is the result of treating d and e as c's recursively until 1 is reached, creating a tree with several to many branches.
Functions
na transform
a movement from a record in (e, n) into (e,1) where n becomes 1 and a becomes a times the n of the (e,n) record. It has also been used to refer to moving n*a records down in a cell.
T
T of number or T(input) is the triangle number function. If our input is 7, T(7) returns the 7th triangle number
T-1, inverse T
the inverse function of the triangle number function that returns the index of a given triangle number. If our input is the 7th triangle number, the function returns 7.
Variables
The map's legend is {e:n:d:x:a:b}, where c is any number that is the difference of two squares, so odd numbers are included. It is the number you want to factor. It is the number that the a and b in an entry multiply to make.
a and b are, to reiterate, the factors of c. a is the smaller factor of c, and b is the larger one.
d is the integer square root of c
e is the remainder of taking the integer square root of c. Unless c is a perfect square, a remainder will be left over.
i is the root of the large square. it is the same thing as (d+n)
j is the root of the small square. it is the same thing as (x+n). i^2 - j^2, difference of squares.
n is what you add to d to be exactly halfway between a and b, and it is the root of the large square. So it takes you from d to the large square.
x is what you add to a to make d. When added to n it makes the root of the small square.
f is what you add to c to make a square. (e is what you subtract from c to make the square below it, f adds to make the square above c.)
g is the square root of c with decimals, opposed to d, which discards decimals.
t is the third coordinate in the VQC, it is a function of x.
u is the base of a triangle that helps us calculate (x+n) for certain c values. simply put, it is a representation of (x+n). 8 times the triangle number of u plus one is x+n.
s was a variable used to demonstrate patterns in (e, 1). See "(e, 1)."
When capitalized versions of the variables are used in comparison to lowercase versions, the capitalized versions refer to the variable's value for the trivial record, and the lowercase variables refer to the values for the nontrivial record.
{e:N:d:X:A:B} (e, N, T) is the trivial element.
{e:n:d:x:a:b} (e, n, t) in this context is the nontrivial element, the prime factorization of c.
____________________________
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72180a No.7691
Rules
Each cell of the grid (e,n) has infinite elements or ZERO elements.
Each cell with one value has infinite elements, since every element can make a new one.
By induction, a cell only needs one value to make infinite values, that's part of the power of this and is why it is a virtual quantum computer as a whole.
The t variable is what will allow you to walk across these infinite elements.
If a grid cell has elements, all elements are constructable from a finite set of root elements.
Thus, only three variables are required to identify an element: e, n and t.
All products of odd numbers and all products of pairs of even numbers are the difference of two squares.
(1, 1) - the key
The values of a and b at 1,1 are related to the length of the longest side in right angled triangles.
The values here can be used to create the entire grid.
The values here determine the values of the rows to the left and right, which determine the values of the whole column.
Columns
Each cell at n=1 contains the roots of products in the column.
If c is a prime number, it will appear in one column exactly once.
If c is the product of two prime numbers that do not equal eachother, c will appear in two cells of one column.
All products (integers) c that are the sum of two squares appear (only) in columns where e=0,1,4,9,16,25…
All factors in a column are factors of the elements of the first cell in their column.
All Fermat primes (except) 3 appear in column one.
(e, 1)
If a number at position t has a factor s, then s is a factor at (t+s), (t+2s) and so on for a at (e,1).
Also, if a number at position t has a factor s at (e+1), then s is a factor at (s+1-t), (2s+1-t), etc for a at (e,1).
n*a and n*b for any c can be found n places apart in the cell at (e,1).
(1, n)
The cells in row one where n=1 have a relationship with the cells 2n to the right and 2n to the left.
Each "a" from the first row equals na because xx+e = 2na and na is half of that. That's BIG part of the KEY
Each element in a cell can be generated by moving up (t-1 = x-2) or down (t+1 = x+2). Other variables can be generated from x.
For more of these rules, see the grid patterns thread.
Useful Equations and Notation
ab = c
dd + e = c
(d + n)(d + n)-(x + n)(x + n) = c
a + 2x + 2n = b
a = d - x
d = a + x
d = floor_sqrt(c)
e = c - (dd)
b = c / a
n = ((a + b) / 2) - d
d + n = i
x = d - a
x = (floor_sqrt(( (d+n)*(d+n) - c))) - n
x + n = j
j^2 = 8*T(u) + 1
f = e - 2d + 1
u = (x+n) / 2
if (e is even) t = (x + 2) / 2
if (e is odd) t = (x + 1) / 2
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72180a No.7692
Code
C#
BigInteger Square Root —— https://pastebin.com/rz1SdACZ
VQC code w/ Bitmap —— https://pastebin.com/hMTtJF6E
PMA's tree generator —— https://pastebin.com/ZH9fSWu2
Original VQC code —— https://pastebin.com/XFtcAcrz
Unity Script —— https://pastebin.com/QgAXLQj3
Unity Script 2 —— https://pastebin.com/Y38nVWgT
Java
Traverse the VQC cells in real-time —— https://anonfile.com/TeH6q3d8bd/VQCGUI_v2.7z
Tree Generator —— https://pastebin.com/VZnQQR2i
VQCGenerator —— https://pastebin.com/Dgu9aP1h
VQC Triangle Number Methods —— https://pastebin.com/NCQ3HK2K
NodeJS
BigInteger Library and Sqrt —— https://pastebin.com/y8AXtFFr
Python
3D VQC [V2] —— https://pastebin.com/wZM5Thzu
Useful methods from CollegeAnon —— https://pastebin.com/d8xZZnm0
Create the VQC —— https://pastebin.com/NZkjtnZL
Fractal cryptography —— https://pastebin.com/XuN4U7Dv
GAnon's Viewable Grid code —— https://pastebin.com/czpK8A4j
Generate any cell in (0,1) and (0,2) —— https://pastebin.com/gRTYpdMU
Generate cells for a (and more) —— https://pastebin.com/iAizgLFF
Generate genesis cell —— https://pastebin.com/GKzcCpMF
Generate positive AND negative genesis cells —— https://pastebin.com/9ixjRyxt
VQC + t —— https://pastebin.com/Lgufk0db
RSA & PGP key wrapper —— https://pastebin.com/vNqnPRJR
Rust
Additional VQC code —— https://play.rust-lang.org/?gist=50def916ad48400bc5d638fbf119ae85&version=stable
Check if a number is prime —— https://huonw.github.io/primal/primal/fn.is_prime.html
Create Bitmap using the VQC Generator [V2] —— https://pastebin.com/zGSusyz5
Generate the VQC —— https://play.rust-lang.org/?gist=6b6beb372b6b931f1abd30642a35a80c&version=stable
Static Java/C# class with all RSA numbers —— https://pastebin.com/XYFpsDWE
Factorization methods (Java)
Binary search for i —— https://pastebin.com/TAt5bDsR
GCDFactor —— https://pastebin.com/70GJSMrv
Calculate factors using -x jumps —— https://pastebin.com/gKX9GW9r
Count down from t of 1c element —— https://pastebin.com/xxYa946V
Mirrors 1c until e=(-x+n^2) —— https://pastebin.com/WJBqPM4P
Shor's Algorithm (enter a random number < c as m) —— https://pastebin.com/RD83RTNc
Other Threads
Fermat's Last Theorem —— https://archive.fo/iTneU
Grid Patterns —— https://archive.fo/isamV
RSA #0 —— https://archive.fo/XmD7P
RSA #1 —— https://archive.fo/RgVko
RSA #2 —— https://archive.fo/fyzAu
RSA #3 —— https://archive.fo/uEgOb
RSA #4 —— https://archive.fo/eihrQ
RSA #5 —— https://archive.fo/Lr9fP
RSA #6 —— https://archive.fo/ykKYN
RSA #7 —— https://archive.fo/v3aKD
RSA #8 —— https://archive.fo/geYFp
RSA #9 —— https://archive.fo/jog81
RSA #10 —— https://archive.fo/xYpoQ
RSA #11 —— https://archive.fo/ccZXU
RSA #12 —— https://archive.fo/VqFge
RSA #13 —— https://archive.is/Fblcs
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72180a No.7693
The fact that we're almost a year into this and we still don't have an easily accessible pastebin for making new threads with is a bit aggravating. https://pastebin.com/VkaTJcX1
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b129f9 No.7695
I apologize for necesitating an emergency bake. I was busy.
In a clearer format (the one I keep) (also, fixed some typos):
post 1, glossary - https://pastebin.com/gWV7vySY
post 2, rules - https://pastebin.com/cE195ptk
post 3, code - https://pastebin.com/heweAtWs
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b1d934 No.7696
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83b459 No.7697
YouTube embed. Click thumbnail to play. The Dimension equals 8?
Q=D5=Minecraft Avalanche
VQC=8D=Mathcraft Avalanche, starting with a single particle of water.
Difference of 3 Dimensions.
E8 H2O
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83b459 No.7698
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83b459 No.7699
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83b459 No.7700
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83b459 No.7701
>>7700
Also duh, I'm jumping ahead.
We're on 14.
Which woulda been perfect for 7700, cuz 7+7=14, and then 7x7=49 and 7^7=823543
Anyway.
14th prime is 43
Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime.[1]
43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 × 3 × 7).[2]
43 is a centered heptagonal number.[3]
Let a0 = a1 = 1, and thenceforth an =
1
/
n − 1
(a02 + a12 + … + an − 12). This sequence continues 1, 1, 2, 3, 5, 10, 28, 154… (sequence A003504 in the OEIS). a43 is the first term of this sequence that is not an integer.
43 is a Heegner number.[4]
43 is the largest prime which dives the order of the Janko group J4.
43 is a repdigit in base 6 (111).
43 is the largest natural number that is not a (original) McNugget number.[5]
43 is the smallest prime number expressible as the sum of 2, 3, 4, or 5 different primes:
43 = 41 + 2
43 = 11 + 13 + 19
43 = 2 + 11 + 13 + 17
43 = 3 + 5 + 7 + 11 + 17.
When taking the first six terms of the Taylor series for computing e, one obtains
∑
i
=
0
5
1
i
!
=
163
60
=
2
+
43
60
,
\sum _{{i=0}}^{{5}}{\frac {1}{i!}}={\frac {163}{60}}=2+{\frac {43}{60}},\
which is also five minus the fifth harmonic number.
Every solvable configuration of the Fifteen puzzle can be solved in no more than 43 multi-tile moves (i.e. when moving two or three tiles at once is counted as one move).[6]
McNugget Number
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b542af No.7702
So if you're in the discord you may have heard about this but I made a little app for you guys to use to navigate the map. I think it can be really useful for those of us who don't like to calculate or make an excel grid every time. It is fairly easy to use as well. It is all in one python file I'm not sure if you need to run it from a terminal but I would do that if I were you. Before you run the file make sure your console window is big enough I couldn't figure out how resize it through python.
Essentially the top left is the map and you can highlight cells based on whether they have the same d x or a value as your starting cell. You can navigate through this map however you want. If you highlight a cell and it has records, they will show up on the right window with other ones in the same cell. You can navigate up and down these records. If you press 'i' while highlighting one, it will get sent down to the bottom detail row. It will stay there until you set a new starting record or delete it. If you press 'h' while highlighting a record that will become the new starting one. I'd recommend typing !help to learn how it works and just play around with it
To create records type 'abd 5 29 12' or the similar with enx or end or others. Screencaps are here
code:
https://pastebin.co m/745cFABb
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b542af No.7703
>>7702
>7702
Also theres definitely room for optimization. I tried to generate the records in a dictionary and then load them so I didn't have to iterate through x values for every pixel in the map but I couldn't get it for some reason and I wasn't concerned about it really so I just generate every pixel. Someone could easily fix that. I plan on making improvements and adding more features I just think this is at a pretty solid state so I want to send it out. Also don't fuck with pressing j or k on a record in the n=0 row. It will crash the thing because I index with x and x is all the same with that so it never finds the next x and I dont feel like adding a whole nother indexing set for n=0 so just understand the patterns there.
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b1d934 No.7704
I've been spending some more time looking into the smooth numbers. I've noticed that given (e, n) the smooth numbers for those records (bigN - n) exists in (e - 2*n, 1). If e is odd, then the smooth numbers will exist as d's. If e is even then smooth number will appear as a. If you jump to (e + 2n, n) the smooth values of those records will match the a's or d's in (e, 1) at t for bigN. Essentially, given a record a, b we get bigN. If e is odd then the d at a[t] = aBigN (e, 1) will be a "smooth" number for the jump (or a + 1, b + 1) in (e + 2n, n).
The smooth numbers of (0, 1) exist in (-2, 1) at t = 1, 4, 9, 16…
The smooth numbers of (1, 1) exist in (-1, 1) at t = 1, 4, 9, 16…
It also appears that the t's for the smooth numbers in (e, 1) exist in (e - 1, 2). Although that is just a preliminary result. I haven't had much time to look into that result.
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b1d934 No.7705
>>7704
The patterns aren't always [1, 4, 9, ..] but offsets.
Take (7, 1). The first 10 smooth numbers are:
[2, 5, 10, 17, 26, 37, 50, 65, 82]
Here the relationship with squares is 2 + 2, 5 + 4, 10+6, 17 + 8.
(8, 1) has first 10 smooth numbers: [4, 8, 14, 22, 32, 44, 58, 74, 92] which has the pattern 4 + 0, 8 + 1, 14 + 2, 22 + 3, 32 + 4 …
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b1d934 No.7706
>>7705
Take cell (3, 6). Moving to the left will put us in (3 + 2*6, 6) => (15, 6).
The first 10 rows in (3, 6) is:
and their smooth numbers are:
{3:6:4:3:1:19}
{3:6:16:9:7:37}
{3:6:34:15:19:61}
{3:6:58:21:37:91}
{3:6:88:27:61:127}
{3:6:124:33:91:169}
{3:6:166:39:127:217}
{3:6:214:45:169:271}
{3:6:268:51:217:331}
{3:6:328:57:271:397}
[0, 108, 540, 1620, 3780, 7560, 13608, 22680, 35640]
While the first 10 rows in (15, 6) are:
{15:6:17:9:8:38}
{15:6:35:15:20:62}
{15:6:59:21:38:92}
{15:6:89:27:62:128}
{15:6:125:33:92:170}
{15:6:167:39:128:218}
{15:6:215:45:170:272}
{15:6:269:51:218:332}
{15:6:329:57:272:398}
{15:6:395:63:332:470}
and their smooth numbers are:
[129, 579, 1683, 3873, 7689, 13779, 22899, 35913, 53793]
Note that (15, 6) has "shifted" one record down, meaning the first cell in (3, 6) (a=1, b=19) is gone.
Each of the smooth numbers in (15, 6) are the d's at (3, 1) where a[t] = BigN.
The big n for a=7, b=37 is 114 and the d at that location = 129 and exists at t = 8.
This means that the t's in (3, 1) where d = smooth number for (15, 6) are: [8, 17, 29, 44, 62, 83, 107, 134, 164]
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b1d934 No.7707
>>7706
Minor typo, pasted the records along with the smooth numbers, but you'll see the difference.
The smooth numbers for (3, 6) (0, 108, …) exists in (3 - 2*6, 1) => (-9, 1) at t's: [2, 8, 17, 29, 44, 62, 83, 107, 134]
Which we can see occur at the same location in (3, 1) as the smooth numbers do for (15, 6).
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4fbd64 No.7708
Continuing with the aan(n-1) work from the previous bread >>7584, have found an alternate way to calculate the triangle base and remainders in some cases for more than the first factor record.
Drawing from these VQC hints, though not sure if related and/or relevant.
>>7636
>Think -1.
>>7639
>The key is how many squares make up the remainder.
All aan(n-1) calculations for (-f,1) and (e,1) will have at least 1 square multiple of aa for the first factor record, and 2 or more for subsequent factor records. Idea being that if we can understand how those triangles and remainders are calculated, we would be able to jump to another record.
Attached pics for c255025 (101^2 * 25^2) show the first 3 factor records where a[t] is 1, 5, and 25.
The "u calc" column is calculated relative to (n-1) as follows:
if a > a[t]: (n-1) - (((a - a[t]) * (n-1))/a) - 1
if a < a[t]: (n-1) + (((a[t] - a) * (n-1))/a) + 1
if a = a[t]: always (n-1)
where "a" is a valid square multiple in aan(n-1), and a[t] is the "a" value from the factor record.
For triangle bases u < (n-1), the a > a[t] formula seems to be relatively accurate as reflected in the "u diff" column for various test cases in both (0,n) and (1,n).
When u > (n-1), however, something else starts to creep into the calculation as can been seen in the a[t]=25 example. Larger a[t] values will have a larger discrepancy, but not yet sure how these are calculated. An "(x)" in the "u calc" column indicates an incorrect value.
The triangle remainders where a[t] is 1 and 5 can also be calculated in terms of (a-a[t]) as shown in the "rm/(a-a[t])" and "sqrt" columns. Again showing the inverse relationship between the "aa" square multiple and the triangle remainder formula. More discrepancies also appear in calculating these remainders as a[t] increases and for u > (n-1) as can be seen in the a[t]=25 example.
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e77daa No.7709
This has completely destroyed my life. It didn't hit me how terrible it was until today, but fitting in enough time to study everything I've studied about it over the past 3 months or so and doing Grid Patterns completely by myself has led to my friends thinking I'm a useless, selfish cunt, my sleep schedule being ruined to the point of it probably affecting me long-term, my university grades tanking, my diet becoming very unhealthy, and in general my mood being very negative. I'll try to stop this from turning into a wall of text and just say that I'll still be around to do mod duties, but unless something big happens very soon, I'm possibly going to have to take an extended break, for my own good.
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b1d934 No.7710
>>7709
Hey man, that's understandable. You need to take care of yourself. You've done a massive job and I'm very impressed (and a bit guilty for not participating as much in the pattern thread). I hope you'll straighten things out.
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d02d29 No.7711
>>7709
Ive found that in my studies I always wind up in that same position after about 3 months or so. Also, think of it like a video game. Ever play a game and you just cant get past one part? But then if you put the game down and come back after a couple of days you beat that level on your first attempt? Take a break. Sometimes we need to get out and see some trees in order to get the inspiration we need to make any progress.
It's easy to want to be 'the one' to figure it all out but we are racing against them, not each other. When I figure it out while you are taking a break I'll include you in a footnote somewhere towards the back of my dissertation :^)
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94c848 No.7712
>>7709
Hello AA, I can relate. I was spending so much time on this that my family life and health was suffering. I'm still thinking and working every day, but I've had to dial back my involvement a bit and make sure the other parts of my life are getting the focus and attention they need. Also, I had to ask for help to quit drinking which was fueling my late night obsessive working till early hours and wrecking my sanity and health. I have 37 days sober today.
I think I can speak for everyone here when I say Thank You for all your work over the last few months. Take the break you need to put your life back in balance, my friend. Love ya!
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b129f9 No.7713
I've taken a few steps on formulating Shor in terms of and linking it to the language of the VQC and I've found that the possible values in the most important step of Shor (period finding) are actually related to N-n.
The possible period values found in calculating Shor's algorithm with random m values from 1 to c-1 all originate from the prime factorization of N-n.
An example, c=253, (the number we are looking at here is the second number in each bracket, which is the period value arrived at when the first number in the bracket is used as m in Shor).
https://pastebin.com/beY9hPx0
N-n = 110 = 2 * 5 * 11 which means we expect to find that a combination of these 3 factors results in every possible period value, and that is what is found in the data. 55, 22, 10, 5, and 110 are period values in the data and they are all products of a combination of 2, 5, and 11.
You find the same thing for other examples (it takes a lot of computing to calculate these examples)
6107, N-n = 2940: (in the attachment, I had to put it into a pdf because 8chan doesn't allow text files)
2940 = 2^2 x 3 x 5 x 7^2, so we expect every period value (second number in the brackets) to have a combination of 2, 3, 5 and 7 as a factor (note, it still counts if it's missing one of these factors from the prime factorization because it can be written with the factor it's missing to the power of 0)
145, N-n = 56: https://ghostbin.com/paste/2cg75
123, N-n = 40: https://ghostbin.com/paste/fqu8u
287, N-n = https://ghostbin.com/paste/7te9u
So the first noted connection between Shor and the vqc happens to be N-n and smooth numbers.
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b129f9 No.7714
A concept you all might find interesting, from the General Number Field Sieve (it is pretty simple if you know what a smooth number is.)
Let's say we're going to look at 3-smooth numbers, numbers which at most have 3 as a prime factor. We can represent all of the 3-smooth numbers as evaluations of:
2^x * 3^y = 3-smooth number
where the exponents determine which number it is. For example, 12 = 2^2 * 3^1
We can represent this in a different notation called exponent vectors (the premise of the notation is simple, don't let that scare you).
Since we know we're looking at 3-smooth numbers, we only need to know the values of the exponents to represent a given 3-smooth number.
2^2 * 3^1 becomes (2, 1). (I haven't confirmed a connection here, but does this look familiar?)
So, our 3-smooth numbers become sets of exponent values. E.g, (3,1) = 24. We can also define multiplication of these "exponent vectors." Since a pair of values now represents a number, we can simplify multiplying these pairs by adding their exponent values instead of calculating the actual multiplication.
(4,2) = 144
(4,1) = 48
(4, 2) times (4, 1) = (4+4, 1+2) = (8, 3) = 6912 = 144*48 (This also defines squaring a 3-smooth number, as in (2,1) times (2,1) = (4,2) = 12*12.
Incidentally (or maybe not), any exponent vector that only contains even exponent values happens to be a perfect square. As in, (4,2) = 12*12, (4,4) = 36^2, (6,2) = 24^2, and so on. (This type of notation is used in GNFS to find one of the nontrivial squares (i^2 or j^2) which, interestingly enough happen to be equal when you are operating in GF(c) where c = ab, a field modulo c. When you are operating in GF(c) (you may have seen Galois fields in my ECC explanations), i^2 = j^2 (mod c) and i^2 - j^2 = 0 (mod c) (because they are equivalent to c, when it's modulo c then it's 0 since c%c=0).
So there you have it. Smooth numbers in Shor, smooth numbers in GNFS in a relatively simple introduction, and N-n as a smooth number.
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b129f9 No.7715
>>7714
Any k-smooth number can be represented this way, this paper introduces the concept with 19-smooth numbers.
An example of this type of notation with a number we're familiar with:
N-n for 145 = 56 = 2^3 * 7^1
So if we define that as a 7-smooth exponent vector with 2 inputs it'd be (3, 1). It's also not the difference of two squares so it isn't found in the grid, at least in positive e and positive n.
As an example, all of the period values for 145 can be represented as one of these exponent vectors.
2 = (1, 0)
4 = (2, 0)
14 = (1, 1)
28 = (2, 1)
The same is true for all N-n from what I have seen so far. All of the period values can be represented in the exponent notation for the prime factorization of N-n, as further proof that N-n's smoothness determines all possible period values evaluated in Shor's algorithm for c.
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b129f9 No.7716
c is b-smooth.
If you write c in exponent vector notation then every c value is in (1,1) because c = a^1 * b^1.
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b129f9 No.7717
Interesting paper - this paper details a factorization algorithm for determining what it has termed Nf(N), or what we would call 2*i, or a+b
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b129f9 No.7718
>>7717
Follow up paper, I like this guy:
His paper includes finding a variable that is equivalent to d or d+1. Then calculating square's difference from c, which is either e or f.
Someone should tell him we simplified his work.
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b129f9 No.7719
for future reference on our variable names (we are working on formulating these papers in the language of the VQC)
d = floored sqrt(c) = sqrt(c)//1 = sqrt(c) with no decimals
g = sqrt(c)
So we'll call the actual square root of c with the decimals g
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b129f9 No.7720
When we formulated this first paper (A-Quick-Way-to-Factor-Large-Semiprimes.pdf) in the terms of the VQC, we found that the VQC language simplifies the approach greatly and requires less steps.
In this first screenshot I have here, Kurwzeg's "Nf(N)" (a polynomial equation with c as the input multiplied by c again, in number theory c is N and pq is ab) is equal to 2*i or 2(d+n) or a+b.
In essence this paper is saying Kurzweg has developed a method of factorization that is equivalent to searching for the value of a+b or 2(d+n). We find that we can greatly simplify his work using our equations.
The equivalent equations in the terms of the VQC:
c = ab
c = i^2 - j^2
His Nf(N) is equivalent to 2*i, so, if we iterate for 2i in the same manner he does ("using MAPLE math program," screenshot two), we can derive the factors by
i = 2i / 2
j = sqrt(i^2 - c)
a = i - j
b = i + j
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7e317b No.7721
>>7712
>>7709
Its amazing that it has come this far. Been following this for a while with a friend, but I really gotta say that this whole thing here is problematic and everyone here should take a break honestly. It says a lot that Chris would let it go this far. Simple as that.
That said, this is the most fascinating experiment in human nature I have ever seen in my life. Someone could get a PHD from this place without ever even doing a math problem to be honest. Simply analyzing the people and their interactions and such would be enough. I encourage you to all just maybe come here once a week or so AT MOST. Also, I encourage Chris to move things along. Things have gone too far imo.
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b129f9 No.7722
Some formulae for deriving Kurzweg's variable k (from solution values j and i so far), in (A-New-Method-for-Factoring-Large-Semiprimes.pdf)
if (c%6) == 1 {
k = ( ( sqrt( (2j)^2 + 4c ) - (c+1) ) / 36) * -1
}
if (c%6) == 5 {
k = ( ( sqrt( (2i)^2 - 4c ) - (c-1) ) / 36 ) * -1
}
in the program "calc," they'd be written as (in the same order as above for the cases of which to use):
define kF(c, j) = (-1*(sqrt((2*j)^2 + 4*c) - (c+1)))/36
define kG(c, i) = -1*((sqrt((2*i)^2 - 4*c) - (c-1))/36)
examples of k values (examples c's from the paper):
kF(34417, 72) = 945
kF(21428053, 594) = ~594964.444
kF(21428053, 594)*36 = 21418720
kG(106577, 369) = ~2950.889
kG(106577, 369) * 36 = 106232
kG(732010841, 29229) = 20333020
In his paper,
G = (2i)^2 = 2(d+n)^2
F = (2j)^2 = 2(x+n)^2
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b129f9 No.7723
>>7722
So, in the second paper, Kurzweg's second factorization method went from being a search for 2i to being a more informed search for 2(d+n)^2 or 2(x+n)^2 based on the remainder of c%6.
Interestingly, (c-1)/6 or (c+1)/6 is always in the ring of Z, which is number theory speak for it's always a whole integer, and which one it is is based on whether c%6==1 or c%6==5, respectively.
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b129f9 No.7724
Also, an idea on what the point of the remainder tree was:
We were told to repeatedly divide each term by 2 until it was no longer a multiple of two. What does that make? A list of odd numbers, which also isolates the primes.
So , hypothesis:
with smooth numbers you are looking at the primes that make up a number by multiplication and with the tree you are looking at the primes in the remainders.
The tree wasn't the solution, it was a hint.
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83b459 No.7725
Sooooo….
Considering what's happening with Linux recently…
Since 2015…
It'd be a hell of a plot twist if Chris was non-other than Linus himself…
And this is his planned "Fuck you, I'll just make another one! I've done it before!" to the SJWs trying to ruin Linux…
And this is how the New One gets Open Sourced.
That'd be fuckin' stellar.
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b542af No.7728
Hey I just made a walkthrough of some of the grid patterns in the grids. Pic related. I hope this works as an ad for my program too. I also hope we can navigate through the grid on with these patterns.
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b129f9 No.7729
Kurzweg's 3 papers all have confusingly similar names, so I'm going to give them distinct names:
(A-Quick-Way-to-Factor-Large-Semiprimes.pdf) = the 2i paper, the 2(d+n) paper (because that's the value he's searching for, in his terms, Nf(N))
(A-New-Method-for-Factoring-Large-Semiprimes.pdf) = the 2i^2 and 2j^2 paper, because this paper contains a description of an iterative search for the values of 2i^2 and 2j^2 in our terms
(A-New-Approach-to-Factoring-Semiprimes.pdf) = the d, e and f paper, because the variables d, e and f all show up in this paper (I'll show how in a moment).
Next I'm going to outline his paper (the d e and f paper) in terms of our equations. I'm going to use greek letters for his variables that don't exactly map to ours because we've almost taken up the entire alphabet, and he introduces a lot of different variables.
A NEW APPROACH TO FACTORING SEMI-PRIMES:
step 1:
g = sqrt(c)
g is a variable we've defined before, this one includes the decimals
step 2:
α = the closest whole integer to g (d or (d+1))
step 3 - realize that there are two unknown values which add and subtract from α to make a and b:
a = α - β
(where β = x or x+1)
b = α + γ (this isn't a y (why), this is a γ (gamma))
(where γ = (x+2n) or (x+2n-1))
step 4 - which become, if we rearrange:
α * (γ - β) - β*γ = c - α^2
In our terms,
β*γ = x * (x+2n)
or
β*γ = (x+1) * (x+2n-1)
Here's where it gets fascinating:
c - α^2 = e or f
step 5, solve for (β*γ) and (γ - β):
β*γ = δ + ε (where δ and ε are an unknown integers)
γ - β = (c - α^2 + δ + ε)/α
δ < α
step 6, eliminate γ from the equations and set δ=c - α^2 (I'm not sure of the exact path of this mathematical jump so I'll figure it out later if it is important):
β^2 + β*(ε / α) - (δ + ε) = 0
step 7, solve for β:
β = -(ε / (2*α)) + sqrt( (ε / (2*α))^2 + (δ + ε) )
step 8, since we know ε / (2*α) must be an integer (because it's defining β and a = α - β), we can get to the value that we need to search for to factorize:
let ε / (2*α) = ζ
β = -ζ + sqrt( ζ^2 + 2*α*ζ + δ)
step 9, rearrange for factors:
a = (α + ζ) - sqrt( ζ^2 + 2*α*ζ + δ ) = (α + ζ) - η
b = (α + ζ) + sqrt( ζ^2 + 2*α*ζ + δ ) = (α + ζ) + η
letting η = sqrt( ζ^2 + 2*α*ζ + δ )
step 10:
α and δ are known from c ( δ = c - α^2 and α is the closest integer to g (d or d+1)), so now it just becomes finding a value of ζ that makes η evaluate to a whole integer.
next, Kurzweg solves for ζ and defines the search as between 0 and 1 (decimals), but I don't think that is the right direction to go with this.
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b129f9 No.7730
>>7729
I'll program an algorithm of this tomorrow.
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3cab20 No.7731
>>7729
We don't have to calculate g to determine whether g is closer to d or (d+1), we just have to see whether e or f is smaller. If f < e then α = (d+1), if f > e then α = d
Kurwzeg has been treading on our territory since 2013 (most recent paper on factorization from what I've seen so far was in 2015).
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abe23c No.7732
>>7729
You're right, that is damn close. I was following his last example in A-New-Approach.. and he almost hits a few of our variables (d+1 instead of d, thus missing our e-value).
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3cab20 No.7733
>>7732
I wouldn't consider it a miss. Using d+1 produces f.
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3cab20 No.7734
Next paper from Kurzweg found:
Groundbreaking.
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3cab20 No.7735
Also, a 2012 paper (much older than the rest) describing a method involving the "integer spiral."
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3cab20 No.7736
A 2015 paper from Kurzweg on it as well.
He is quite the rising star.
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3cab20 No.7737
Ulrich H Kurzweg factorization papers list (to eliminate confusion) (they are all describing different algorithms and approaches):
November 1, 2012 - (Factorizing-Semiprimes-with-the-Integer-Spiral.pdf)
August 2013 - the search for 2(x+n)^2 or 2(d+n)^2 paper (A-New-Method-for-Factoring-Large-Semiprimes.pdf)
Christmas (December?) 2013 - the search for 2(d+n) [N(f(N)] paper (A-Quick-Way-to-Factor-Large-Semiprimes.pdf)
January 2015 - d, e and f paper, (A-New-Approach-to-Factoring-Semiprimes.pdf) (hereby renamed the zeta search paper since it is a search for the value of a variable I've renamed to zeta ζ for our purposes)
August 2015 - Factorizing with Q primes (Factoring-Large-Semiprimes.pdf)
April 7, 2016 - (UNIVERSAL-CURVE.pdf)
Who knows where he's gotten by now.
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3cab20 No.7738
ZetaSearch (UHK) —— https://pastebin.com/iUVg7q2u
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3cab20 No.7739
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b129f9 No.7740
research to sort through.
http://algo.inria.fr/seminars/sem00-01/morain.html
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b129f9 No.7741
Kurzweg contacted.
Location of forum and of us was not revealed, only mathematical concepts shared in order to prove we are serious and are making enough progress (even to the point of improving on current research).
Pursuit of more of his research and his expected interest in our research was made clear.
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abe23c No.7742
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b542af No.7743
>>7742
Made a new python script to look at records. It has way more features.
Now you can:
- view d, x, a, c, (d+n), (x+n), f, t, grids. (f grids look cool they're like a spiral)
- track and highlight records
- mark any cell on the grid
- view all e,n,d,x,a,b,c,f,x+n,d+n in the list view on the right
I highly recommend it. If it doesn't run on your computer or something I could help you out with the settings or something.
https://pastebi n.com/aZGz2RHF
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b542af No.7744
>>7743
start it in a terminal and make sure the window is big enough or resize the settings or change the terminal font size. If you want to learn type !help basic
Then from there there will be a tutorial type path to go !help commands or !help map
Really cool tool
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b129f9 No.7745
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0e79d3 No.7746
It is a lookup via the x values in row 1.
It is about finding how to make the lookup with column -f and e.
Something about the product of squares and triangles. I(t) stands out. Once you c it, you cannot un-c (i)t.
In The End, it is a lookup.
No more secrets.
Sneakers.
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0e79d3 No.7747
>>7743
Outstanding.
One pattern that might be important…
Negative x values in row 1.
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83b459 No.7748
>>7747
The Return of Senpai…
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b542af No.7749
>>7747
x does x values, shift +x shows -x values. I noticed they were always the same. I thought about consolidating them to one button but I figured people should know.
Here is the record
9, 17, 6, 5, 1, 45
If we go along the n=1 row for -x of our original record, we get this pattern on the bottom row.
c = 65, 84, 105, 128, 153, 180, 209, 240, 273, 308, 345, 384
change in c = 19, 21, 23, 25, 27, …+2, +2, +2,
at e = 9, the same e as the original record, the value is 153.
153 - 128 = 25
180 - 153 = 27
so I guess the derivative at that point is 26.
Otherwise e increments by 2, n doest move, d increments by 1 and so does a and b.
t, f, and x+n seem to be constant (d+n) increments by 1.
Also people there are still some bugs I'll fix them.
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930093 No.7750
According to the -x value hint, maybe look at x - n values since (-x + n) = (x - n) and see the u that that creates.
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930093 No.7751
Just a quick look:
c287
X = 15, N = 128
(X+N) = 143, U = 2556, (X+N)^2 = 20449
(X-N) = 113, U = 56, (X-N)^2 = 12769
f = 2, e = 31
(31, 1, 7) -> {31:1:113:13:100:128}
(31, 1, 8) -> {31:1:143:15:128:160}
(-2, 1, 8) -> {-2:1:111:14:97:127}
(-2, 1, 9) -> {-2:1:143:16:127:161}
|
(31, 1, 0) -> {31:1:15:-1:16:16}
(31, 1, 1) -> {31:1:17:1:16:20}
(-2, 1, 1) -> {-2:1:-1:0:1:-1}
(-2, 1, 2) -> {-2:1:3:2:1:7}
287 = 7 * 41, x = 9, n = 8
(x+n) = 17, u = 8, (x-n)^2 = 289
(x-n) = 1, u = 1, (x-n)^2 = 1
The patterns say, look, I, the solution am here! But can we bring it out?
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b542af No.7789
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dc77e5 No.7790
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9983d2 No.7792
>>7751
correction: U value of X+N is 71
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b129f9 No.7793
if (e, n, t) = (e, n, d) then sqrt(2d) ~= sqrt(x)
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8b4129 No.7794
>>7793
This is explainable with algebra. If d=t, depending on the parity of e, 2t will be within 1 of 2d. The square root of a number is very close to the square root of itself plus or minus 1.
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b129f9 No.7795
>>7746
>>7747
This hint is greatly connected with these. Why calculate 2d from e - (-f) - 1? Because now 2d applies to the entire column.
Also, T-1(d) is the same value plus or minus one as sqrt(2d)
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8b4129 No.7797
Since I couldn't find any triangle visualization tools written in Java, I've been putting one together myself. It isn't finished. If anyone did already write one I must have missed it. Nobody will probably use this so it doesn't matter. Here it is, anyway. https://pastebin.com/3nDs75dy It relies on this GridCell object https://pastebin.com/HEC87GAQ
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b129f9 No.7798
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8b4129 No.7799
>>7798
With colours now (that was fucking horrendous to get my head around): https://pastebin.com/4CE3tirj
I just wasted another 8 hours straight doing something that probably isn't going to solve the thing. I haven't even eaten dinner and it's already past midnight. I have a problem, and I think the only way I'm ever not going to keep doing this is either if I quit altogether or if we finally solve it. I don't know which of those is going to come sooner than the other.
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af9884 No.7800
>>7748
Tops, my love for the will never waiver.
Maths without Art is like POTUS without genius.
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af9884 No.7801
>>7749
>>7799
>>7798
>>7797
>>7795
>>7794
>>7790
The best and most pragmatic advice I can offer is to use known numbers at scale as well as what you are doing.
Reconcile an earlier post with a HUGE drop in BTC.
Everything is connected.
You are on the verge.
100%
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4fbd64 No.7802
Was reviewing (0,n) in terms of squares and triangles.
Pics attached for c144 are the (0,n) entry record, it's na record in (0,1), and an annotated view of (0,1) in terms of the a and d formulas.
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4fbd64 No.7803
>>7746
Expanded the search into -x for the aan(n-1) hint.
c145 and c287 examples attached show how the aan(n-1) calculation for each factor record in positive x equals the product of (-f,1) a[t] and (e,1) a[t].
In negative x, however, these values differ as shown in the highlighted rows.
We could force these values to be equal by adjusting the x offset between the -f and e columns by 1. For example in c 145, aligning the x=-7 record with x=-8 instead of x=-6 would result in an aa product of 500 and match to the factor record.
This would require a rethinking of how -x records align between the -f and e columns.
On the other hand, this difference in aa product vs aan(n-1) from the factor record is correct and offers additional information to be analyzed.
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4fbd64 No.7804
>>7803
Condensed output attached for c145, c287, and c6107 showing just the relevant factor and -x factor records.
Highlighted "d diff" columns represent difference between d values in -f and e columns for the solution factor records.
Add both highlighted values together and you will get 2x.
Which is the same "d diff" as the starting c record and it's -x offset.
For c145, where starting x=11.
c records "d diff" = 0 + 22 = 22
prime records "d diff" = 4 + 18 = 22
Similar for other examples, and makes the case that the aa product and aan(n-1) differences in -x are correct.
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43930d No.7805
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4fbd64 No.7806
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8b4129 No.7807
>>7801
We've been on the verge for almost a year but okay
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43930d No.7808
An interesting relation I found while working on the new hints that could become a quicker way to calculate integer square roots:
TM1(c-1/2) = d or d-1
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43930d No.7809
>>7808
Clarification:
TM1((c-1)/2) = d or d-1
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43930d No.7810
>>7809
>>7808
I just realized that the TM1 function relies on the integer sqrt function, so nevermind. But still an interesting relation.
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43930d No.7811
Another triangle identity:
k = an integer
k^2 = 2T(k) - k
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8b4129 No.7812
I've been avoiding talking about this because I know I'm not going to get an answer that actually explains jack shit but what was the point of the rm2dnm1 thing from RSA #10? n0 is somewhere between f/8 and 1. We want some number between them that is greater than n and less than x+n. That divided f value is a staircase number. You put it into the rm2dnm1 function and it gives you a number that isn't 0 because it isn't going to equal the correct u value. We never seemed to do anything with that value aside from checking whether it was zero. What was the point of that entire thing? If n0 is never going to equal n, we're never actually going to use that function for the sake of checking that a number gives a remainder of 0 and is thus u. So we do want the remainder, and we do want a specific value from the staircase number, but what are we even using them for?
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8b4129 No.7813
Now you put a and b in through terminal and you can iterate through all cells with the same x+n. For even n odd x, it takes one away from n (to make it an odd square in the center) and adds the difference to f.
Triangles - https://pastebin.com/Kjm6jhZE
GridCell - https://pastebin.com/KRg2QTH9
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43930d No.7814
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8b4129 No.7815
>>7813
>>7814
Max x+n is 649, by the way, because I needed to make it all actually fit on the screen so the minimum button size is one pixel. I don't know if that's big enough for what we're doing but VQC has never elaborated about what "big enough" is. It takes a very long time to load this since it has to make a maximum of 421201 squares and figure out whether they're fs or not (which was pretty complex, and works in a while loop iterating f by 8 each time). It's not very useful for iterating a and b at that scale (a-b=(x+n)*2 so to get the next (x+n) you just add or subtract one to a and b). In fact I haven't successfully waited through one with an x+n of 649. It might take a few hours. I don't know. x+n of 135 took a little over 10 seconds.
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Post last edited at
9f86d9 No.7816
>The best and most pragmatic advice I can offer is to use known numbers at scale as well as what you are doing.
>Reconcile an earlier post with a HUGE drop in BTC.
>Everything is connected.
And theeen you see that we're looking for the element in (e,1) where x + (e a value) - (-f a value) = original d value.
for c145 here's the calc:
original d value = 12
(e na transform) x value = 11
at x = 7, we have the following calc: x= 7 + (25) - (20) = 12 = original d value.
which gives us d = x + a, 12 = 7 + 5
So my idea is to use the original d value as the target that we're trying to make x+(e a)-(-f a) add up to. Have we already done this lads? Just thinking the clue through again and working it through.
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8b4129 No.7817
>>7815
>>7813
Here's a version that displays the (d+n)(d+n) square beside it in the fashion of VQC's diagrams. It doesn't work with very big numbers, or numbers that are quite far apart. That's because of how much larger (d+n)(d+n) usually is than (x+n)(x+n) (pic two is a good example of why it might not be super useful for bigger numbers (note that this is before I scaled them the same)). I might turn it into a bitmap generator at some point (I would be super grateful if someone else did but I know nobody will). So while this working with big numbers would obviously be ideal, it seems like the only way we'd get it working is with bitmaps. But I'm not sure.
(x+n)(x+n) and (d+n)(d+n) visualization in Java - https://pastebin.com/TV4Ud7j7
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8b4129 No.7818
>>7817
Now you can view the na transform and bign cells (if their x+ns are odd), and go back to the original. https://pastebin.com/rBEFuU05
Would definitely not recommend the bign button for large numbers (because of what I explained in that quoted post about (d+n)(d+n)) unless you remove the (d+n)(d+n) functionality, but even then it depends on the (x+n)(x+n) size.
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8b4129 No.7819
>>7818
The bign thing probably isn't working when you view a BigN cell for an even a even b cell, by the way..
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43930d No.7820
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8b4129 No.7821
>>7820
That was all I was going to do aside from potentially turning it into a bitmap generator actually.
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43930d No.7822
>>7821
I know, but that's all you have to do to handle this well. Just take breaks.
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8b4129 No.7823
>>7822
>that's all you have to do to handle this well
I'll handle this well when something happens that justifies the amount of time I've put into this.
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83b459 No.7824
>>7823
What kind of VQC Proof would you like?
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43930d No.7825
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83b459 No.7826
>>7825
Sure, we were thinkin' that.
Fiiiiiiiine.
But what about my valtrex medication?
My husband has YET to pick any up.
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8b4129 No.7827
>>7825
>>7824
>>7826
"when something happens that justifies the amount of time I've put into this" != proof. If I didn't think this was real, why would I have spent all that time? That would be fucking moronic. What I mean is finding the solution. That would justify me destroying a friendship and completely neglecting university because I was spending too much time doing Grid Patterns.
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83b459 No.7828
>>7827
I remember friends… be glad you only have VQC to sink into.
You want the solution… but you haven't earned it and we're not at a place where we need to have it finished yet.
What are you going to school for?
Something that will be meaningless when this is successful?
Even if you're going for something that will still exist… I'm an artist.
You have way more of an advantage by doing this, hopefully.
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8b4129 No.7829
>>7828
Super constructive, thanks Topol
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83b459 No.7830
I'm only as good as what I have to work with.
Want me to send you money for a whore?
I'd… I might throw some cash at that, but I need proof.
No Proof = Refund.
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43930d No.7831
c6107
{23:2976:78:77:1:6107} (23, 2976, 39)
{23:1:18641629:-6107:18647736:18635524} (23, 1, -3053)
{23:1:18653843:6107:18647736:18659952} (23, 1, 3054)
{-134:1:18647657:-6108:18653765:18641551} (-134, 1, -3053)
{-134:1:18659873:6108:18653765:18665983} (-134, 1, 3055)
α = 18641607
β = 9322268
γ = 18647657
δ = 18647712
γ - α = 6050
δ - γ = 55
γ - α - c = -57
α - (-134, 1, -3053)[b] = 56
α - (-134, 1, -3053)[a] = -12158
(α - (-134, 1, -3053)[a])/2 = -6079
α - (23, 1, -3053)[b] = 6083
α - (23, 1, -3053)[a] = -6129
α - (23, 1, -3053)[b] - α - (23, 1, -3053)[a] = -46
6107[x] = 47
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43930d No.7832
c34117
{261:16875:184:183:1:34117} (261, 16875, 92)
{261:1:581950858:-34117:581984975:581916743} (261, 1, -17058)
{261:1:582019092:34117:581984975:582053211} (261, 1, 17059)
{-108:1:581984790:-34118:582018908:581950674} (-108, 1, -17058)
{-108:1:582053026:34118:582018908:582087146} (-108, 1, 17060)
α = 581950598
β = 290983839
γ = 581984790
δ = 581984713
γ - α = 34192
δ - γ = -77
γ - α - c = 75
α - (-108, 1, -17058)[b] = -76
α - (-108, 1, -17058)[a] = -68310
(α - (-108, 1, -17058)[a])/2 = -34155
α - (261, 1, -17058)[b] = 33855
α - (261, 1, -17058)[a] = -34377
α - (261, 1, -17058)[b] - α - (261, 1, -17058)[a] = -522
34117[x] = 75
This hasn't been ironed out, as one can see.
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83b459 No.7833
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dc77e5 No.7834
I give you guys presents but I'm not sure anyone opens them.
The only one who takes me seriously is VQC.
I guess it's because I connect dots in a non-linear fashion.
And because I have the barest understanding of the math you guys do.
You guys are amazing.
Seriously. You guys are smart as hell.
But it takes all kinds to complete the puzzle.
I need you.
And you need me.
My "crumbs" will stand the test of time.
Of that I am certain.
My mathematical intuition has never failed me.
I have the box, but not the key.
I cannot open them by myself.
So here are more presents for those anons who wish to open them.
May you find some inspiration!
#1.
>https:// medium.com/@thoughttheory/lets-see-how-deep-the-rabbit-hole-goes-9af5f9896941
=
>http:// archive.is/64L2h
#2.
>https:// www.academia.edu/7489568/The_pythagorean_relationship_between_Pi_Phi_and_e
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83b459 No.7835
>>7834
Are you "rambles in randomly labeled, yet complexly generated math" guy?
If yes…
When did VQC take you seriously?
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dc77e5 No.7836
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83b459 No.7837
Shall Capwn?
If yes, chat me up on faybo.
Let's catch you up.
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8b4129 No.7838
>>7834
>I give you guys presents but I'm not sure anyone opens them.
>I have the barest understanding of the math you guys do.
I don't mean to be patronizing, but, I mean, duhhhh. I don't know who you are because your IP hash only has three posts associated with it, but chances are if you're complaining about nobody reading your posts because they aren't the same kind of math that the rest of us are doing, it's because you haven't done the following:
(a) read all of the threads so you understand the grid (it's not difficult, it's just time consuming - I was going to work on a simple guide in June (before that too) but nobody ever wanted to help me so it never happened). VQC explained it pretty well at the beginning of the first thread. We're finding a and b, the factors of c, c being any arbitrary number of your choice. c has a bunch of variables associated with it. You can grid these sets of variables with e as the x axis and n as the y axis, and they create infinite sets. Relationships between cells of variables (different a and b pairs) can be used to factor any arbitrarily large number. Understanding the multitude of patterns will lead us to the solution. Go read the threads. You don't turn up to a calculus class with a chemistry textbook and pass the class, man.
(b) figure out just how related your math is to the grid - if VQC is taking you seriously, maybe it's important stuff, but if you don't even understand the grid, how do you actually know it's related? Intuition is a strong thing, but you have to back your shit up with facts, anon. If we're all talking about (x+n)(x+n) and you're trying to relate the golden ratio to the Mandelbrot set, we're in completely different worlds. Apply it to the concepts we're all studying or we're not going to have a use for it (at least with our current objective).
(c) now that you'll know how the math we're doing works, you'll have the terminology and the context to apply your math to it in such a way that you can explain where you're coming from. We're working explicitly on what VQC is trying to explain to us. If you post something that seems like it doesn't have anything to do with that (like weird graphs with lots of geometric shapes in seemingly arbitrary places like that one anon), obviously you're not going to get very much attention. If it is related, explain in terms that we understand (i.e. with our math). Let's say you found out that f divided by d is equal to a (that's definitely not true but it's an example). Let's say you found it because you're super into geometry and you were messing around with the grid and found this weirdly shaped line. If you didn't understand the grid (which you said you don't), you'd be telling us "hey guys, there's this weird shape here and you really need to know about it" then all you're doing is showing us a weird line. What are we meant to do with that? We've seen lots of weird lines and none of them got us anywhere. If you understood the grid, you would be able to say "hey guys, f/d=a, isn't that neat". Then we'd actually know what you're talking about.
tl;dr: read the threads
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b129f9 No.7841
>>7832
>>7831
A thread specifically about this type of thing: >>7839
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3cab20 No.7845
I've got a new idea and it's simpler than what I was working on earlier. It's putting the remainder tree and the grid together and it also unifies the "the solution is recursive" and "the grid does all the work for you" hints.
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3cab20 No.7846
The grid took me from (d+N) to (d+n)
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3cab20 No.7847
you start at the odd column (it's either f or e), where t=-(d+N-1) then you take sqrt(2d) and it equals c, then you take sqrt d and it gives you another value and then you set that value as x and it will send you down the column, and then you take sqrt(d) again and use that as x, then keep doing that, sometimes it'll have you switch columns
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3cab20 No.7848
Also, (d+N) - (d+n) is N-n because d is the same
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3cab20 No.7849
It doesn't work for all semiprimes yet (need to look into how it works more, but here's a look so far
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3cab20 No.7850
It can't factorize large semiprimes yet. I think it's missing something.
Interestingly it instantly terminates when you enter a prime, ie it takes one step to terminate on known rsa number factors. So if I can find the missing piece of this it could be a prime test too.
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8b4129 No.7851
>>7850
Without seeing your code, it doesn't take into account
>(e,1)
>(0,n)
>triangles
>diagonals
etc so if you generate triangle diagrams and output the respective (e,1) cells, just as an example, during your process, it might display some patterns.
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3cab20 No.7852
>>7851
Do you have an idea on what to add to it?
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8b4129 No.7853
>>7852
Well for a start, if you're starting in whichever column is odd, chances are it's different for odd e and even e, so you might just have to add one or divide by two somewhere. Just in general, you aren't utilizing every concept. While (0,n) and (e,1) might not be used in one particular solution, VQC said the three solutions he's aware of involve either (0,n) or (e,1) or diagonals. So as much as you could potentially find another solution, I think it's far more likely that you've found something that you're meant to use in conjunction with the other concepts. So maybe if you run your algorithm and every time you calculate a new cell you also find that cell's (e,1), for example, it'll have some important value in it, or its triangle configuration will have something in common with the solution cells, or something. My point is to start analyzing this at a deeper level. One other idea is that you could work backwards. If you're taking a cell and setting the square root of its d to x, you could take xx and xx+1 as potential d values in the cell that leads to the solution cell.
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3cab20 No.7854
Here's the code.
https://pastebin.com/sEse8cxm
try exploring setting x = f or f-1 (depending on whether the column is even and odd), and try exploring setting x to root of f and root of e. Also, we should figure out what a diagonal is.
Also, I have no idea how to mix 0,n into this.
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b129f9 No.7855
There was a "ghost in the machine," so to speak, as to the reason why some of the records are invalid in the screenshots, but the code has been corrected to reflect the original idea of the movement from (-(odd column), 1, -(d+N)) to (col, 1, -(d+n). Also, it wasn't terminating in one step, I just forgot to print out the movement, but Chris has already said an instant prime test will be included with the solution.
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83b459 No.7856
>>7800
Grazie grazie.
I told Olga Vishnevsky that I'd promote her whenever I could.
I was almost tempted to hit up my The Professor to give him a update.
Buuuuut he'll find out eventually.
After all, someone needs to teach the Maths + Arts class we were talking about before this all started.
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b542af No.7857
Slightly off topic, but I think that he chose these variables for a reason. I think that the N in supposed
to represent the natural numbers. I say this because for e=0, you can multiply any record by a constant and it will represent another record.
On a side note, is this the offset we're looking for?
Notice how for the records e = 85, it is the origin of the parabola, where in the f values, the origin of the parabola is in e=84.
They're offset by one
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b129f9 No.7858
VQCGUI revision 3, includes source
https://anonfile.com/37C6mej1b4/VQCGUI-0.0.3_7z
try navigating from a[t] = N record to a[t] = na record, you will see amazing patterns in the values on the right.
sqrt(2d) has an intricate relationship with the x values.
(yes I know there's a typo, too late to recompile).
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b129f9 No.7859
Enumerate the patterns in the first row (and into negative x).
It will be something that was there that you didn't c that will trigger it.
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b129f9 No.7860
I will come back to clarify the other by the end of the week but briefly. Using the values of RSA 100 just as a large number example is a suggestion. In column e, the values at (e,1) for each element includes a value for a[t] which is an. The value bn is at a[t+n]. At (-f,1) the value a(n-1) is at the same value x in that cell as "an" for (e,1), the value b(n-1) at cell (-f,1) is one element less than bn at (e,1). This difference is key. It is not the only key, as you are seeing. I have found three, not including yours. Those three are in row 1, column zero and the side by side diagonal cells from the origin. There may be infinite keys.
Two sets of equations that run together and then merge, lock and key.
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b129f9 No.7861
diagonal = one thing that is one unit apart from another thing, the offset is one
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abe23c No.7862
>>7859
Are you paraphrasing VQC or did you figure it out? Some of the lines appear to be quotes by VQC from past threads.
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b129f9 No.7863
>>7862
just paraphrasing vqc
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b129f9 No.7864
//using the diagonal to find pairs that are one row apart
c1541
e=20, f = 59
sqrt(e) = 4, sqrt(f) = 7
sqrt(f) - sqrt(e) = 3
2d = e + f - 1
{20:732:39:38:1:1541} i[t] = 771; j[t] = 770; sqrt(d[t]) = 6; sqrt(2d[t]) = 8; f[t] = 59
{-59:731:40:39:1:1541} i[t] = 771; j[t] = 770; sqrt(d[t] = 6; sqrt(2d[t]) = 6; f[t] = 140
140 - 59 = 81
difference between f[t] in (e,N, t) and (e, N-1, t) = 81
{20:6:39:16:23:67} = 1541; i[t] = 45; j[t] = 22; sqrt(d[t]) = 6; sqrt(2d[t]) = 8; f[t] = 59;
{-59:5:40:17:23:67} = 1541; i[t] = 45; j[t] = 22; sqrt(d[t]) = 6; sqrt(2d[t]) = 8; f[t] = 140;
140 - 59 = 81
sqrt(140) - sqrt(59) = 4
difference between f[t] in (e,n, t) and (e, n-1, t) = 81
{20:1:770:38:732:810} i[t] = 771; j[t] = 39; sqrt(d[t]) = 12; sqrt(2d[t]) = 17; f[t] = 1521; c[t] = (d+N)^2 - d^2
{-59:1:770:39:731:811} i[t] = 771; j[t] = 40; sqrt(d[t]) = 27; sqrt(2d[t]) = 39; f[t] = 1600; c[t] = (d+N-1)^2 - d^2
1600 - 1521 = 79
sqrt(1600) - sqrt(1521) = 1
{20:1:154:16:138:172} f[t] = 289; c[t] = (d+n)^2 - d^2
{-59:1:132:17:115:151} f[t] = 324; c[t] = (d+n-1)^2 - d^2
324 - 289 = 35
sqrt(324) - sqrt(289) = 1
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b129f9 No.7865
I'm making the most progress working backwards, seeing that it's not about going from c to n, it's about going from d and e to n and N.
"Two sets of equations running together."
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b129f9 No.7866
since f=(x+1)^2 at (e,1), f increases in squares by t of the opposite parity of e. if e is even, f increases in odd squares, and if e is odd, f increases in even squares.
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b129f9 No.7867
eventually you realize x+n is so special because it's a view of the diagonal, of the key
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b129f9 No.7868
diagonals
difference of squares
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83b459 No.7869
From the Discord:
how much effort do you really need to put into a tree?
they kinda… just… do on their own… y'know?
you can go all bonzai if you like, or train 'em to make bridges…
but a tree's gonna do it's do whether you do your do or not
it's like a…. fractal… binary… self-replicating algorithm.
so where do you plant the seed?
let's say you have an effect or decision in this
just… y'know… find yourself in such a position
you have the seed, and the ground… plus the environment
but let's say this is a tree that can grow anywhere and will adapt to every situation
where do you want it?
Mmmmmmmminecraft.
Basically, you could put a palm tree on the top of mount everest.
er… no
it would take the form of whatever it takes to survive right there
you're not like… GOD all of a sudden
you get that seed into the ground, the Tree will do its do… however it HAS to do and ONLY that way way in such an EXTREEM environment
the "tree" at the bottom of the marianas trench has gotta look nutz
ooooor the one on mars. or jupiter. or the sun. or a comet.
Just a matter of getting The Seed there.
Ham Fisted Terraforming
so whaaaaat is the Seed "plugged into"?
a server? an id? a portfolio of accounts? a control panel of some sort?
math is sexy, but in this analogy… what is the vqc and what is the encryption? what's the seed, ground, and… is the VQC the tree? The Ground?
Is The Grid the ground that we put The Seed into to see The Tree produced by the seed?
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83b459 No.7870
>>7869
Or is it like this?:
The Grid is the The Environment.
The Ground/Fertile Soil is the VQC.
The Seed is the Encrypted… Thingy.
Put The Seed into Ground to see The Tree.
The End is a Forest of Trees.
Maybe the "Leaves" are the "Remainders" or something.
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8b4129 No.7873
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bd5068 No.7876
>>7873
AA, this is the best I summary I have from my work on the (f-1)/8 method:
How to find the two adjacent Triangle numbers: Take the SQRT of (f-1)/8. This will be the larger of the two Triangle numbers we need, let's call it T2. The smaller staircase number, T1, is simply the T1- 1. Here's an example. For c6107, (f-1)/8 = 16. SQRT 16 = 4. So our first staircase number T2 is 4, and T1 is 3. T2 + T1 = 10 + 6 = 16.
My question is what to do with the remainders. We have remainder from (f-1) mod 8, and sometimes we also have an additional remainder from SQRT ((f-1)/8). So we end up with our two staircase numbers, and at least one remainder to deal with, sometimes two remainders.
The idea is that those two triangle numbers multiply, and that multiples of them will equal our correct (x+n) square. The cool thing about this is that as you work outward from the center of the x+n square, the pattern grows in a very orderly fashion.
I could use some help trying to figure out how to handle the two sets of remainders, but VQC said that we had come VERY close to completing the pattern, which would then lead to the grid shortcut.
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bd5068 No.7877
>>7876
>The smaller staircase number, T1, is simply the T1- 1
Typo here lads. Should read:
The smaller staircase number, T1, is simply T2- 1. (the next smallest triangle number)
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bd5068 No.7878
>>7873
Here's one almost complete, but still trying to figure out the edges like VQC asked. Not sure how the remainders play into completing the edges. There must be a way that fills the x+n square perfectly, once we know how to correctly use or dismiss the remainders. Oops, I see a symbol in there, wonder where all those ancient cultures got that good luck symbol from?
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8b4129 No.7879
>>7876
>>7878
What does that picture with the mini yellow and green triangles represent? Is it c? All I've ever seen going through past threads is the picture itself and not an explanation, so I haven't been taking note of it since I have no idea what it is. It doesn't look like (x+n)(x+n) because of the whitespace. But if it's c, I haven't ever seen anyone break it down into smaller parts that aren't dd+e.
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6fe22c No.7880
>>7879
Hey AA! The diagram is the area of (x+n)^2. The two triangle numbers are represented by yellow (T2) and green (T1). The blue units are the remainders from (f-1) mod 8.
I think the key is adding the two bases of the staircase triangle numbers together, so in this case it's 4+3=7. For c6107, the correct u is 42. So in this example, 7 * 6 = 42. So the correct u value is a multiple of 7. In this case, u and u1 are 42 and 41, which add to 83, which is the correct x+n value. The correct area of this x+n square is 83^2 = 6889
I think the rm(2d-1) comes into play here by being able to give us a lock on the correct multiple of u that gives us a perfect square, 6889.
Here's the breakdown from VQC:
>>6185
>The solution to this problem introduces a new form of algebra where two concurrent forms of equations run side by side and then merge.
>Take some time to think about what that means.
>Have you seen this approach before?
>What could it look like?
>Many new solutions often seem obvious in hindsight.
>In fact many new designs seem to simplify in many varied approaches to design.
>Does it seem obvious in hindsight that in order to solve a multivariate equation, that something new but similar to what we have always done, would be the solution? Just taken in a new direction? Expanded thinking.
>The two sets of equations take the problem and simplify it. Together they handle the "lock and key" nature of the problem/solution, particularly when c is divisible by 1, c, and two other prime numbers, such as in RSA.
>The two forms of equations that merge together handle staircase numbers where the base of one staircase, is one unit longer than the other.
>The analogy to Fermat's Last Theorem. Two objects that seem to be completely unrelated were proved to be the same object.
>Two seemingly different 'fields' will be used side by side and merged to create an elegant solution. Again, this can only be done in reverse, using the assumption that P=NP. I only saw at the end of over seven years work. Anons have got much further in six months than I would have. I would have walked away in frustration back in the day but you anons here have been amazing.
>Take some time to think what this will look like and how the diagrams (especially animated) might show this.
>I think things will start moving quickly.
>This will be new mathematics. It will make more sense than how this problem has been approached up until now.
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279dad No.7881
>>7879
Here's the steps for a test program:
start with c
get d, e, and f
calc (f-1)/8
calc SQRT((f-1)/8) = base T2
define base T1 as T2-1 = T1
T1 + T2 = potential u value
iterate potential u value looking for lock using rm(2d-1) formula, basically looking for a perfect square.
hopefully find a lock for the correct (x+n)^2 value.
Basically the correct u value should be a multiple of the combined bases of T2 and T1. Remainders may need to be accounted for as well, not sure yet.
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b129f9 No.7882
>>7880
>>7881
An example of the staircase numbers:
in the even column, (x+n)^2+3 = (f-1/8) + ((f-1/8)+1)
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8b4129 No.7883
>>7882
Where did you get that equation from?
(18:1:5) = {18:1:49:8:41:59} f=-81
(1+8)(1+8)+3=(80/8)+((80/8)+1)
84=/=21
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b129f9 No.7884
>>7883
It was typed hastily while I was typed, but the pattern observed. Add a division by 4 on the left side and it works.
84/4 = 21
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b129f9 No.7885
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6feebe No.7886
>>7885
Heres all the info I could figure out for the A grid. It looks like at most points there are at least like 5 dimensions to work into. Horizontal movement, diagonal, parabolic (x2), parabolic again if at the origin, then increasing t values for a given cell. I want to do these for every grid. The e+2a, n+1 movement is common though so I wanted to do the A grid first.
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b129f9 No.7887
rsa100u = 529865753494301776968715634328960133662340771465
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b129f9 No.7888
>>7881
Chris dropped a different formula at the very end of RSA#12 for N that I didn't notice.
We've been using
N = (c+1)/2 - d
but
N = (c-1)/2 - x
also works
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8b4129 No.7889
>>7884
And this is just in (e,1), yes? Because you should be specific about that. Otherwise you would have solved it for even e.
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b129f9 No.7890
>>7889
Yes, just for (e,1). I apologize for the false positive by not clarifying that.
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b129f9 No.7891
Also, 2 values of c at (e,1) (a different idea)
2 values of c in both columns in -x and +x
145:
{1:61:12:11:1:145} (1, 61, 6)
{1:1:10368:-145:10513:10225} (1, 1, -72)
{1:1:10658:145:10513:10805} (1, 1, 73)
{-24:1:10500:-146:10646:10356} (-24, 1, -72)
{-24:1:10792:146:10646:10940} (-24, 1, 74)
34117:
{261:1:581950858:-34117:581984975:581916743} (261, 1, -17058)
{261:1:582019092:34117:581984975:582053211} (261, 1, 17059)
{-108:1:581984790:-34118:582018908:581950674} (-108, 1, -17058)
{-108:1:582053026:34118:582018908:582087146} (-108, 1, 17060)
rsa100c:
{61218444075812733697456051513875809617598014768503:761302513961266680267809189066318714859034057480651323757098846024549192056136964455981270339102876:39020571855401265512289573339484371018905006900194:39020571855401265512289573339484371018905006900193:1:1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139} (61218444075812733697456051513875809617598014768503, 761302513961266680267809189066318714859034057480651323757098846024549192056136964455981270339102876, 19510285927700632756144786669742185509452503450097)
{61218444075812733697456051513875809617598014768503:1:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306382919000431748126203278565987540269446653259579647945903160561369722164795555272230598393346522221773:-1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306384441605459670659563814184365672906876371327694609326591818469864302287758814225128252393697214227912:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306381396395403825592842742947609407632016935191464686565214502652875142041832296319332944392995830215636} (61218444075812733697456051513875809617598014768503, 1, -761302513961266680267809189066318714859034057480690344328954247290061481629476448827000175346003069)
{61218444075812733697456051513875809617598014768503:1:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306385964210487593192924349802743805544306089395809570707280476378358882410722073178025906394047906234051:1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306384441605459670659563814184365672906876371327694609326591818469864302287758814225128252393697214227912:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306387486815515515726284885421121938181735807463924532087969134286853462533685332130923560394398598240192} (61218444075812733697456051513875809617598014768503, 1, 761302513961266680267809189066318714859034057480690344328954247290061481629476448827000175346003070)
{-16822699634989797327123095165092932420211999031886:1:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306384441605459670659563814184365672906876371327694609287571246614463036775469240885643881374792207327717:-1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006140:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306385964210487593192924349802743805544306089395809570668259904522957616898432499838541535375142899333857:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306382919000431748126203278565987540269446653259579647906882588705968456652505981932746227374441515321579} (-16822699634989797327123095165092932420211999031886, 1, -761302513961266680267809189066318714859034057480690344328954247290061481629476448827000175346003069)
{-16822699634989797327123095165092932420211999031886:1:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306387486815515515726284885421121938181735807463924532048948562431452197021395758791439189375493591339997:1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006140:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306385964210487593192924349802743805544306089395809570668259904522957616898432499838541535375142899333857:1159163035527489297252269855748911245456985761764903865191919139010631678686397433667992819640306389009420543438259645421039500070819165525532039493429637220339946777144359017744336843375844283346139} (-16822699634989797327123095165092932420211999031886, 1, 761302513961266680267809189066318714859034057480690344328954247290061481629476448827000175346003071)
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b129f9 No.7892
Also another thing worth noting, the b value at the record in (e,1) where a=N, b=N' (shadow N)
shadow N = 2d+N
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cb22e0 No.7893
Hello GA! Here is the big grid image you requested.
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b129f9 No.7894
>>7893
Tempted to try but I'm not even gonna bother trying to open that.
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47ad18 No.7899
Now this makes sense because the x values change based on the column being even or odd
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8b4129 No.7900
>>7899
There's a full parity chart here >>7386
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47ad18 No.7901
a prime number appears once (2^(1-1)) in a column.
a product of two primes appears twice (2^(2-1)) in a column.
a product of three primes appears four (2^(3-1)) times in a column.
a product of four primes appears eight (2^(4-1)) times in a column.
a product of five primes appears sixteen (2^(5-1)) times in a column.
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47ad18 No.7902
focus on solving it for odd x+n and it will expand into all 4 solutions.
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398ad7 No.7903
Introducing the grid and the diagonals then moving to a series of odd x+n hints was not pointless. It's crucial the final step of the journey is solved organically and not given away.
The x+n hints are one solution and will lead to the grid solution.
It will all make sense in hindsight.qGncp
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8b4129 No.7904
>>7903
>introducing the diagonals
Other than a code comment mentioning diagonals, have they really been introduced to any significant degree?
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83b459 No.7905
YouTube embed. Click thumbnail to play. >>7903
Single post… talks like Chris… not same id tho.
qGncp takes you Down Under tho…
https://youtu.be/QgncP-f3XVs
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abe23c No.7906
>>7901
I believe this can also be visualized in (e, c) where c is the product. It's tied into the number of chains in that row, although I haven't quite figured that part out yet.
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abe23c No.7907
>>7906
I've been suspecting for a while that VQC has actually been dropping hints for all three keys, mixed in with each other. I believe the smooth numbers is part of one key, the x+n triangle is part of another and that some of his other hints belong to the third part.
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abe23c No.7908
I've been busy with life for a while, but I did have some realizations the past few weeks.
I can't believe I missed the sqrt(2d), it's obvious now, but it's how you find the triangular base of d. Take a triangle n(n-1)/2 = k. To find the triangular base you do 2k = n(n-1), then the square root will be sqrt(2k) = sqrt(n(n-1)). Floor this number and you will have (n-1).
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abe23c No.7909
>>7907
Yeah here I suspect aan(n-1) belongs to either the smooth numbers key or the third key.
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83b459 No.7910
>>7907
Smooth, Trangle, and Squares, eh?
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83b459 No.7911
>>7910
In case it wasn't obvious… <;3=
Also, don't forget to re-check auto-update.
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6feebe No.7912
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b129f9 No.7913
>>7912
Why did you want that so much?
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473c10 No.7914
Create diagrams for examples -> see the patterns.
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473c10 No.7915
c = 6107
d = 78
e = 23
f = 134
(d+n)^2 {
d^2 = 6084 //first square in structure
f is divided into two pieces, 67+67
e is divided into two even pieces with one left over, 11+11+1^2
d^2 + e + f = 6141 //next square in structure
(n^2 - 1) + last piece of e = n^2 //next square in structure
d^2 + e + f + (n^2 - 1) + 2d(n-1) = (d+n)^2 //the large square
}
(x+n)^2 {
f is divided into two even pieces with two pieces, one and one left over
(n^2 - 1) + one of the leftover pieces of f = n^2 //first square in structure
(n^2 - 1) + f + 2d(n-1) = (x+n)^2 //the smaller square
}
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83b459 No.7916
>>7915
That's super pretty!
Who is this? One of the nerds or has a new player appeared?
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6feebe No.7917
>>7906
>>>7906
>This is interesting too. Look at xx + e = 2na
>If you set a = 1, then xx + e = 2c because n = c
>>7913
Sometimes this is the best way to view it. It's in a grid for a reason right? I threw out my old pc and lost that pic and I missed it sorely
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6feebe No.7918
>>7917
sorry about that first part forgot I was working on something..
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83b459 No.7919
>>7916
Hmmmm… I woooonder if Chris is ip hopping.
Incognito crumb dropping…
Something to do while Q's busy, I suppose.
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4fbd64 No.7921
>>7915
>d^2 + e + f = 6141 //next square in structure
d^2 + e + f = 6241
same as (d+1)^2 or 79^2
nice diagrams!
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9f86d9 No.7922
>>7915
Nice work on this diagram, Anon!
Alright, I have an idea lads.
In the linked c6107 diagram, (n-1) = 35
Let's derive the staircase numbers, as I explained here: >>7881
(f-1)/8 = 16, T2 = 4 , T1= 3, T1+T2 = 7
The 2d(n-1) rectangles are 2730 + 2730, or 2 * 78 * 35
35 = (n-1)
T1 + T2 * iterate = correct (n-1)
7 * 5 = 35
So (f-1)/8 gives us the staircase triangle number bases to add together, and then multiply out looking for a lock. It will scale properly upward, even with huge c values.
Obviously we need to test some other examples, but deriving the T2 + T1 staircase numbers from f , and then using it to iterate/solve for (n-1) works in this c6107 example.
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b129f9 No.7923
>>7922
In its current state, this doesn't scale and it doesn't reach a correct n-1 value for several examples.
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ea7e9b No.7924
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83b459 No.7925
>>7919
>>7924
Oh look, another unique id…
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abe23c No.7928
>>7915
25921
>>7924
204646843863289
Slow your horses VQC, no need to spoon feed us! I still need some time to process it and make sure I got it right.
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93da3c No.7929
Transpose—
The transpose of a given matrix is formed by switching the columns and rows.
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93da3c No.7930
{0:1:2:3:4:5}
{1:2:3:4:5:6}
{2:3:4:5:6:7}
{3:4:5:6:7:8}
{4:5:6:7:8:9}
{5:6:7:8:9:10}
{6:7:8:9:10:11}
{7:8:9:10:11:12}
{8:9:10:11:12:13}
(9:10:11:12:13:14}
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8b4129 No.7931
>>7930
Those aren't valid cells though
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b129f9 No.7932
Was watching some videos and reading some literature on the Riemann Zeta function today. It's really fascinating stuff. There's a lot of calculus and number theory behind it, but basically if the Riemann Zeta hypothesis is true, then you can calculate the exact number with no error of how many primes there are beneath a given integer.
You can already do this with the more accurate version of the prime number theorem and a formula that gives you the amount of error (calculated with the zeros of the Riemann Zeta function), but nobody is sure it's correct because it depends on the Riemann Zeta hypothesis.
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b129f9 No.7933
>>7932
Correction: "with no error" -> "with an extremely small margin of error about the equivalent of a calculation."
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b129f9 No.7934
Hey look it's our friend mod 4
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b129f9 No.7935
Then you find it's all connected
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e2aefa No.7936
Noob here, just wondering, what c value is implied in
>na and nb for any c can be found n apart in the cell at e,1?
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e2aefa No.7937
I'm not sure if I should be throwing gardening tools at a grid cell but GCD seems to fit really well there
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e2aefa No.7938
Wouldn't it be amazing if dark matter didn't exist and the grid did all the work for us?
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e2aefa No.7939
I was really shitfaced last night and I could have sworn there is a pattern of n being a factor of the a values in the cell at e,1 and that n-1 had a pattern of being a factor of the a values in the cell at -f,1
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83b459 No.7940
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83b459 No.7941
Hey Chris!
Since the parade was pushed back… are you still coming stateside?
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8b4129 No.7942
>>7936
>what c value is implied
"any c"
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b129f9 No.7943
>>7942
If you look at the patterns of n in a[t] you find pairs of elements of the n we're looking for multiplied by different a's and b's for a different, smaller c, that are separated by n for that c's elements
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b129f9 No.7944
If you could calculate two multiples of n where the coefficients of n are not multiples of eachother you could calculate n by doing gcd(na, nb)
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b129f9 No.7945
Kind of like the GCDFactor algorithm, but intelligent navigation. This may be the lookup.
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b129f9 No.7946
These particular patterns may be coincedence but this is the approach I'd like to be investigated:
c21428053:
N=10709398
n=38
So we want to find a way to find multiples of 38 in e,1 (work backwards).
In e,1 if we look for n and its multiples, we do find
{412:1:318:14:304:334} a = n*8 t=8
{412:1:470:22:448:494} a = n*13 t=13
8*13 = 104
104's n value = 5 and these elements are 5 elements apart.
So we find our n times a different set of a and b for a different c with elements that are that c's n apart at e,1.
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b129f9 No.7947
>>7946
and gcd(n*8, n*13) = n
so if two multiples of n are found, n can be split from them efficiently (unless the two coefficients are multiples of eachother, as in 7 and 21)
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abe23c No.7948
So it's been a while since I posted much, I've been busy looking over patterns in the grid, but with >>7915 something hit me. What if we've been doing this wrong. We're trying to triangulate (x+n)^2, but we only have f and 2d remainders right? What if we could increase it? What if we could add more information to our data?
I've attached an image that shows my idea. If we connect (d + n)^2 with (x + n)^2 at nn, we have a new square that contains more information that we have. The equation for this square is:
(d + n + x)^2 = nn + dd + 2d(n - 1) + 2d(n - 1) + f + 2 + f - 2 + 2dx
This can be simplified to:
nn + dd + 2d(2n + x - 2) + 2f + 1
In this "upper" square the dd will cover the entire outside of the triangle, meaning the triangle base will be smaller than the u of dd. Essentially, we have a new square and an upper limit of the triangle base of (x+n).
Another thing is that our dd square will now occupy one part of the new square, while xx will occupy the opposite side.
I've also been a bit huffing about the fractal VQC has been talking about, but now I think I'm starting to see it. If we combine the squares as in the attached image we can now see what could potentially be a fractal. I'm not entirely sure how one would map it / graph it, but it's a start.
I do feel like something clicked, but I'll be honest and say that we've all had that feeling before.
A legend for the image:
In the upper left corner you see the dd square with the f/2d extension on the side (n=6) along with the nn square shared between (d+n)^2 and (x+n)^2.
In the lower right corner you see xx and the extended f/2x around it.
As for what we're trying to do, which is find (x+n)^2, this will exist inside of this (d+n+x)^2 with nn in the center, think of it like our original (x+n)^2 = nn + 2d(n-1) + f - 2 equation, except this is inside of dd + 2d(n-1) + 2dx + f + 2.
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abe23c No.7949
>>7948
Attached is an image showing the coloring of the (d+n+x)^2 square.
The outer layer is dd, f + 2, 2d(n-1), 2dx, 2d(n-1), f - 2 and nn in the middle.
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c5d0a6 No.7950
HOW DOES THE GRID ENCODE INFORMATION?
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8b4129 No.7951
Getting back into it a bit. I found a pattern in regards to f/8 being less than or greater than the x+n triangle base u. It seems that there are specific j values which always seem to create an f/8 value which is greater than u. In this image, the numbers are the j values which, together with every i within a range of i values, create a cell with an f/8 greater than its u. The i constraints are the blue text beside each block.
>>7950
HOW DO I TURN CAPS LOCK OFF?
Another joke answer would have been to say UTF-8. I don't know if you're VQC or someone else but I don't see how this question is meant to help other than in hindsight.
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43930d No.7952
And the name of the city from that day shall be: "THE LORD IS THERE."
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b129f9 No.7953
an interesting observation: N%4=n%4 generally
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8b4129 No.7954
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2344ac No.7957
Some random food for thought:
c=ab
2 inputs
infinite solutions
infinite wrong solutions
1 right solution - two primes
encode solution not as a number
but as a pattern, algorithm, approach towards the number
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83b459 No.7961
>>7957
Encode as a Fractal?
An Algorithm that is Self-Replicating and Binary, perchance?
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83b459 No.7962
YouTube embed. Click thumbnail to play. Disclaimer: this post and the subject matter and contents thereof - text, media, or otherwise - do not necessarily reflect the views of the 8kun administration.
83b459 No.7963
YouTube embed. Click thumbnail to play. Disclaimer: this post and the subject matter and contents thereof - text, media, or otherwise - do not necessarily reflect the views of the 8kun administration.
b129f9 No.7964
this is so sad, Alexa factor integers in logarithmic time
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b129f9 No.7965
www.wired.com/2011/01/partition-numbers-fractals/
"Fractals solve the problem of calculating partitions"
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b129f9 No.7966
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b129f9 No.7967
The Part contains the Whole.
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b129f9 No.7968
(c, n) spreadsheet.
same diagonal line patterns as the grid.
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b129f9 No.7969
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b129f9 No.7970
What do we get when we sort numbers by their distance from a square instead of as a line?
2, 5, 10, 17, 26, 37, 50, 65, 82, 101
3, 6, 11, 18, 27, 38, 51, 66, 83, 102
4, 7, 12, 19, 28, 39, 52, 67, 84, 103
5, 8, 13, 20, 29, 40, 53, 68, 85, 104
6, 9, 14, 21, 30, 41, 54, 69, 86, 105
7, 10, 15, 22, 31, 42, 55, 70, 87, 106
8, 11, 16, 23, 32, 43, 56, 71, 88, 107
9, 12, 17, 24, 33, 44, 57, 72, 89, 108
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b129f9 No.7971
Approaching the grid as a fractal
N of 5 = 1
N of 17 = 5
N of 37 = 13
65 = 5*13
See pattern.
Understand.
Then build.
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b129f9 No.7972
[iterating d for e=31], relevant c=287
32
35
40
47
56
67
80
95
na = 56
so e,1 in our grid analyzing every value of d in d^2 + e for us. understanding why the grid is configured the way it is is a good exercise.
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b129f9 No.7973
We want to master the pattern of factors of a[t] in e,1.
Every n value that exists in column e is a factor of a[t] in e,1.
>>6579
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b129f9 No.7974
e,1 as a catalog of all valid n values.
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b129f9 No.7975
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b129f9 No.7976
>>6580
What does "position of column 0" mean?
From our even column, (f or e), distance from column 0 can be expressed in jumps of 2n (where n=1), but not for the odd column.
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b129f9 No.7977
anyone ever notice how 145 is the sum of squares?
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b129f9 No.7978
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83b459 No.7979
>>7977
145=64+81
145=8^2 + 9^2
So… Polite Squares? Or would there need to be a third?
7,8->113
8,9->145
7,8,9->194
8,9,10->245
7,8,9,10->294
8,9,10,11->366
Then what?
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8b4129 No.7986
VQC, please read this post and respond to it
As far as I can tell. I've finished getting all of the patterns and concepts together in the Grid Patterns thread >>6506 here. I have a couple things I wanted to ask about.
For whatever range of reasons, none of the other anons have been helping, and none of them have been proofreading or checking that I'm correct and that I haven't missed anything. That means it's probably likely that I missed something or that maybe something is incorrect. I know you of all people will know if anything is right or if anything important has been missed. There's a lot of information in that thread, but would there be any chance you might have the time to go through and check everything?
Secondly, in your explanations of (x+n)(x+n)=nn+2d(n-1)+f-1, you introduced us to n0 and the guess triangle base made of f/8 or f/(8*something). As far as I could tell going through the threads, you never actually seemed to do anything with either of these values. If n0=n and guess base=u, you can construct the (x+n)(x+n) square, but you even said yourself that we know n0 won't equal n and we know the guess base won't equal u. After explaining that, you stopped talking about n0 altogether, and only mentioned the guess base a bit cryptically. So what was the point of those variables?
Thirdly, with the grid patterns thread done, do you have any newer advice as to what we should be looking into? Is there anything specific (as in looking at this concept and that concept at the same time) that we should be doing that we can now that everything's in one place?
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b129f9 No.7987
>>7986
I'm thinking fractals. That has to be what we are missing here. It's a way you can turn that massive search space into nothing—because the same patterns that apply to the massive apply to the small, in a fractal.
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4343de No.7988
What happens when equations are evaluated in higher dimensions?
c = 15105
123 = floor_sqrt(-14883 + 244i)
Re: 38! + 1
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83b459 No.7989
>>7979
Hmmmmmm….
8,9
8,9,10
8,9,10,11
8,9,10,11,12
etc etc
Jumps?
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f8a399 No.7990
Why are a and b defined as i-j and i+j?
What is the geometrical meaning behind it?
c=i^2-j^2 or is it
c=i^2+ij-ji-j^2
Keep in mind j is always < i
What does a and b MEAN in this context?
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8b4129 No.7991
>>7988
>>7990
Read the threads
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83b459 No.7992
Riemann Zeta + Mandelbrot
http://www.dhushara.com/DarkHeart/RH2/RH.htm
Riemann Zeta + Non-Mandelbrot Set Fractals
ttp://primepatterns.tumblr.com/tagged/Riemann-zeta-function
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032baa No.7993
>>7992
Finally found the PDF, those equations on the site are impossible to r e ad.
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83b459 No.7994
>>7993
"Lookup in gaps", you say…
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b129f9 No.7995
>>7986
Also, why do you think the grid patterns thread is done
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b129f9 No.7996
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b129f9 No.7997
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8b4129 No.7998
>>7995
Because I've gone through all of the threads and put everything from each one in there. Why do you think it isn't done?
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b129f9 No.7999
>>7998
There's plenty of other grid patterns to look at that haven't been fully enumerated.
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8b4129 No.8000
>>7999
Then enumerate them and put them in the thread yourself.
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83b459 No.8001
>>8000
Holy shit!
Calm yer feckin' tits!
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8b4129 No.8002
>>8001
I'll "calm my feckin' tits" when getting a giant two-month-long set of work done doesn't get a response of "you have more work to do". I'll calm down when I'm not the only one who does that work (I'm not the only one who is meant to work on it by the way, don't know if anyone realizes that). I'll calm down when suggesting that we work on something together for once rather than hiding off in our own little research corners completely ignoring everyone else doesn't get a response (this is a direct quote) of "who cares" on Discord. This is ridiculous. Give me one good reason not to ditch this board and all of you lazy pricks and figure this out by myself, Topol. I might as well considering how little interaction there is between any of us that isn't just mindless chatting on Discord. I'm over being told to calm down when every time I do anything useful here I either get completely ignored or I get this bullshit.
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b129f9 No.8003
>>8002
You're real entitled, you know that?
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8b4129 No.8004
>>8003
What do you think I feel entitled to exactly?
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b129f9 No.8005
>>8004
You're going about this as if you've earned the solution, as if you deserve more. You're too obsessed with the endpoint to the point of putting your friends down just because they don't work on what you want them to.
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83b459 No.8006
>>8002
You're just being unnecessarily aggressive.
Also, I not Jan and the PMA/VA-duo working on this more often than not.
Sure… Minecraft sorta kinda fucked off for whatever reason…
But to claim that you're the only one doing anything is asinine.
You're lashing out. Calm yer tits.
You haven't done this on your own and left to your own devices you wouldn't do it, anyway.
I'm not saying you're not "reasonably frustrated with this whole affair".
But you're not some sort of "uniquely frustrated" where you should be throwing these fits and snapping at mufuggaz.
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8b4129 No.8007
>>8005
>you're going about this as if I've earned the solution
How am I doing that? Topol told me to calm down. I told him why I'm not calm. Everything I'm saying is backed up with facts. I'm not just having a big emotional rant. These are genuine issues (to varying degrees).
>point 2: nobody helped me with grid patterns
Now if everyone explicitly told me "we don't think this is useful, maybe you should do it yourself", maybe I wouldn't mind so much. You actually said multiple times that you would help me with it (so did a couple of the others) and yet you didn't do anything. So this isn't me putting people down because they don't do what I want them to. This is people saying they will do something and never doing it.
>point 3: nobody is working together
I'm not the only one who has complained about this. Several other anons have. Isee was one. I think he was complaining about it on Discord. I suggested we work together on something for once and the only response I got was "who cares". That's a thing that happened. Do you think that's a useful outlook for everyone to have in regards to working together?
Now how am I acting entitled? Are any of the things I said objectively incorrect?
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8b4129 No.8008
>>8006
When did I say I was the only one doing anything? I said I was the only one working on one thing in particular. And then when I said I was done, someone told me to do more work (that they could do themselves, might I add). Also, I can admit I did snap that one time (that was generally a shitty period) but the only snapping I've done today is calling people lazy pricks. Nothing else I'm saying isn't based purely around facts. They might be angry facts, but they're facts.
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83b459 No.8009
>>8008
Sweet, you've acknowledged you snapped at mufuggaz.
Took Chris 7 years to do this…
And yeah, when you finish one thing and there's more that needs to be done… what kind of response do you expect?
"Great job on that one thing! Your job here is done. Please join us in the clubhouse to rest on your laurels!"
Like I said, your not unreasonably frustrated.
But you're not uniquely frustrated and we don't deserve to be the butt of your anger and frankly, neither does Chris.
I'm not saying don't be human.
But if you want a word battle, let's duke it out in the EZ Bake.
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8b4129 No.8010
>>8009
>And yeah, when you finish one thing and there's more that needs to be done… what kind of response do you expect?
When it's something VQC told all of us to do, and it therefore isn't just my job, I don't expect a response of "there's more work to do, go do more work".
>But you're not uniquely frustrated and we don't deserve to be the butt of your anger
All I'm doing is pointing out things that I think are problems. If there's a bit of anger in there, it isn't for the sake of making people upset.
>and frankly, neither does Chris.
Would you like to point out where I got angry at Chris? Because as far as I'm aware I didn't do that.
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83b459 No.8011
>>8010
There you go saying you're the only one doing something again…
And you've seen my try to herd the cats into playing with the same ball of yarn.
You're dealing with maths-people.
It's complex.
We get it. You're upset. Quit lashing at us.
Yeah: >>7986 <<< there you are being pissy and making entitled commands.
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8b4129 No.8012
>>8011
How the hell is that pissy? He misses postss addressed to him pretty often. That's why I made it redtext.
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83b459 No.8013
>>8012
Jesus, you sound like you're new here!
I've made bomb ass points before that he didn't acknowledge at the time.
IF he mentions something I've worked on outside of saying he likes my style… it's when it's coming into play.
For starters… let's look at another pattern.
Have you NOT noticed "someone" ip hopping and making posts?
Sometimes they respond to someone, and sometimes they seem to be in their own little world…
Haaaaave you not figured out what's going on with that, yet?
You are the only one here who can see the ip hashes, after all.
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83b459 No.8014
>>8012
Basically, you'll get a lot farther with this if you treat VQC like Q.
I've posted things that Q didn't acknowledge, only to give the nod to someone else a hundred breads later.
But can you make demands of Q? No.
Should you throw a tantrum and threaten to nuke the place if Senpai doesn't give you the attention you feel you deserve? No.
Pic related.
You've blown off some steam.
Do you feel better?
Can we all go back to playing nice?
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8b4129 No.8015
>>8013
No offense to whoever posted these if they're new and they're just firing off whatever ideas come to them, but is there anything we can actually use any of these posts for?
>>7950
>>7957
>>7988
>>7990
I don't think VQC posted any of those. They're the kinds of musings we all had at the beginning, which makes me think it's a newfag with a dynamic IP or a VPN. When VQC has crumbs, he posts more specific stuff like >>7746 this. Whatever the case, I really don't see how I was acting pissy towards VQC.
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83b459 No.8016
>>8015
Aaaaah you little faggot.
Why'd you leave out the one with the clue in the e-mail?
And let's Occam's Razor this…
It would take an incredibly versed maths-troll to pull some convincing shit out of their ass that we'd "fall for".
Look at the pattern.
Here's another example: Look at how ebot does their schtick.
<;3=
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8b4129 No.8017
>>8016
>the one with the clue in the email
Where? I don't see one.
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83b459 No.8018
>>8017
"lookup in gaps"
>>7993
(You really ARE new here! WAKKA WAKKA!)
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b129f9 No.8019
Okay, but if the goal is to rethink our approach to mathematics as a way of rewriting it, then why would any musing be unwelcome? None of them are things that have been completely explored
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8b4129 No.8020
>>8019
Maybe read my post again because I never said they were unwelcome. I said I don't think VQC posted them because they're musings and VQC posts more specific hints about variables.
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4fbd64 No.8021
>>7988
>Re: 38! + 1
38! + 1 = 523022617466601111760007224100074291200000001
Is a semi-prime with factors 14029308060317546154181 × 37280713718589679646221
Interesting write-up and sample code at https://codegolf.stackexchange.com/questions/8629/fastest-semiprime-factorization
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4fbd64 No.8022
>>7988
>c = 15105
>123 = floor_sqrt(-14883 + 244i)
Relevant records:
entry c: (221,7431,61) = {221:7431:122:121:1:15105} = 15105; f=24;
na: (221,1,61) = {221:1:7552:121:7431:7675} = 57032925; f=14884
Rewriting the floor_sqrt in terms of our variables:
123 = floor_sqrt( -(f-1) + 2di )
where f=14884, and 2d = 244
shows a connection to the d value in the (-f,n) space at:
(-24,7430,62) = {-24:7430:123:122:1:15105} = 15105
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2344ac No.8023
Imagine playing chess.
Every piece has a specific pattern/permutations in which it can move/exist.
Solution to the game is check mate - a specific pattern amongst some pieces.
Superimpose piece patterns to get all possible patterns for all pieces.
On every move discard those patterns that dont lead to check mate.
Play the game.
At the begining there is a starting pattern amongst all pieces.
And a superposition of all possible patterns.
As the game progresses and moves are made, solution space shrinks.
Everytime some cell gets occupied by some piece, solution space shrinks.
On every move evaluate if this specific pattern (can) leads towards check mate.
Does it make sense?
Can we apply it to our problem?
Pieces are equations,
Check mate is c=ab,
Patterns are grid patterns?
Row 0 is a superposition of all possible patterns at every step?
Everytime a cell gets occupied/calculated….???
Just some thoughts, maybe it helps someone.
Will probably work on the analogy further as I can see some resemblance.
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2344ac No.8024
Without any information or sense of what the best move is, of what the best pattern to follow is an algorithm would still reach the solution-check mate, but by randomness.
So, how do we evaluate which pattern in any moment is the best, optimal?
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2344ac No.8025
Dont mind me, just thinking out loud :-)
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83b459 No.8026
>>8024
So… be "steps ahead".
Then get so fast at it, it's as if you pull the answer out of the Quanta.
Kinda like what a VQC does…
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b129f9 No.8027
>>8024
>>8023
>>7957
It is the unity and enumeration of all grid patterns.
>Enumerate the rules.
>Win.
>The solution to this problem introduces a new form of algebra where two concurrent forms of equations run side by side and then merge.
>The two sets of equations take the problem and simplify it. Together they handle the "lock and key" nature of the problem/solution, particularly when c is divisible by 1, c, and two other prime numbers, such as in RSA.
>The two forms of equations that merge together handle staircase numbers where the base of one staircase, is one unit longer than the other.
Two threads in a program, one starts with c=ab, the other starts with c=1c. The equations run independently and encompass all grid patterns, then eventually merge.
c=ab {
d = sqrt(c)
e = c - d^2
f = 2d+1-e
n = (a+b)/2-d
x = d-a
(d+n)^2 - (x+n)^2 = c
(d+n) + (x+n) = b
(d+n) - (x+n) = a
a[e, 1, t] = na
b[e, 1, t] = na+2(x+1)
a[-f, 1, t] = (n-1)a
b[-f, 1, t] = (n-1)a+2(x+2)
}
c=1c {
d = sqrt(c)
e = c - d^2
f = 2d+1-e
N = (c+1)/2-d
X = d-1
(d+N)^2 - (X+N)^2 = c
(d+N) + (X+N) = c
(d+N) - (X+N) = 1
a[e, 1, T] = N
b[e, 1, T] = N+2d
a[-f, 1, T+1] = N-1
b[-f, 1, T+1] = N-1+2(d+1)
}
The equations keep enumerating patterns until they merge.
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83b459 No.8028
>>8026
Also, the Opponent is Watson.
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83b459 No.8029
>>8028
Or DeepMind, if Go is your game.
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b129f9 No.8030
>>8027
cont'd
c = ab {
[1] the entry (e, 1, t+pna) where p is any multiplier of na will contain a multiple of na in a[t]
in other words, na will be a factor of a[t] in that element
[2] the entry (-f, 1, t+1+p(n-1)a) where p is any multiplier of (n-1)a will contain a multiple of (n-1)a in a[t]
}
c = 1c {
[1] the entry (e, 1, T+pN) where p is any multiplier of N will contain a multiple of N in a[t]
in other words, N will be a factor of a[t] in that element
[2] the entry (-f, 1, T+1+p(N-1)) where p is any multiplier of N-1 will contain a multiple of N-1 in a[t]
[3] a[-f, 1, T+1+1(N-1)] = N*c
a[-f, 1, T+1+1(N-1)] / a[-f, 1, T+1] = c
}
They will merge when enough patterns are enumerated. Continue enumerating these patterns -> reach solution.
A question to answer (to define the equivalent pattern for the ab thread). In (-f, 1, t+1) where a[t] = (n-1)a, what defines the multiple of (n-1)a that appears at (-f, 1, t+1+(n-1)a)?
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b129f9 No.8031
>>8030
Excuse the notation.
Notation introduced here:
a[e, n, t]
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b129f9 No.8032
Two independently running sets of equations that apply every pattern to trivial and solution values respectively.
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b129f9 No.8033
>>8030
Note for clarification: the N's and n's used here are from c only since we're working in row 1
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739004 No.8034
>>7899
>>7900
https:// mathrodite.quora.com/Constructing-a-Parity-Truth-Table-for-the-Interval-Between-Perfect-Squares
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83b459 No.8035
>>8034
Hello person who is totally new and posting for the first time!
"Mathrodite"
It is to kek.
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8b4129 No.8036
I'm going to take that break I mentioned now. Good luck people. See you in a month or two (or earlier if something happens).
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47d6d1 No.8037
>>8036
From a lurker, brainlet anon. Thank you for attempting to ennunmerate all of the hints in an organized manner. Hell, you’ve kept the board followable.
The chans are a breeding ground for disorganized but intuitive thought processes. You have been fighting against its natural state. Take care of yourself. That goes for all of you.
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566843 No.8039
Here is an analysis of the (x+n) grid
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266807 No.8040
A staircase number is an (odd) number composed of one number added to the number less than it.
To find the staircase numbers for an odd value, we add one to the value then divide it by two. Then the number is equal to the result added to the result minus one.
Calculating this for the number we started with, would make two familiar values. Adding two side by side (t aligned) x values in e,1 and -f,1 would also make a staircase number.
When na is odd, what do you do to find an identifier for the element where the x is equal to one of the staircase numbers for na? And if na is even, for n-1?
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266807 No.8041
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b129f9 No.8042
>>8041
>>8040
I was trying to continue my system of equations earlier but I couldn't figure out what determines the multiple of na that appears at t+na
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b129f9 No.8043
Equation threads cont'd:
c = ab {
[3] a[-f, 1, (t+1)+(n-1)a] = (2d+1)[t+1] * (n-1)a
a[-f, 1, (t+1)+(n-1)a] / a[-f, 1, t+1] = (2d+1)[t+1]
}
c = 1c {
//since c is equal to 2d+1 of the na transform record at T+1 in cell -f,1, c appears as our multiple of (N-1) when we go (N-1) elements down
[3] a[-f, 1, T+1+1(N-1)] = N*c
a[-f, 1, T+1+1(N-1)] / a[-f, 1, T+1] = c
}
//a factor of 2d+1 of t in -f,1 is added when we go na cells down
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b129f9 No.8044
>>8043
Clarification:
(notation is being pushed to its limits here), pattern [3] applies to going (n-1)a and N-1 elements down from the -f,1 transform record where a[t] = (n-1)a or N-1
t of this record is written t+1 since it is one element below the na transform record in e,1, which we derive from x or X using the t from x formula
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a26807 No.8045
T-24hr.
Blackout in the Red Room.
Highlander 2.
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a26807 No.8046
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83b459 No.8047
>>8045
>T-24hr.
~10pm UTC…
>Blackout in the Red Room
10 days of Darkness?
Red Room… Twin Peaks?
RR…
>Highlander 2
I thought there could only be 1?
Hmmmm… also, considering what's going on with Assange and Ecuador…
I wonder what hands are being played right now…
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a26807 No.8048
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83b459 No.8049
>>8046
Dubya? Hopefully Cheney, too…
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83b459 No.8050
>>8048
43… 42… you being polite?
I'll chill for a bit to see if there's more to this. ^_^
Also, hello Senpai (directly)!
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a26807 No.8051
>>8047
<3
This one is for you.
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83b459 No.8052
>>8051
Yer an ip and trip hoppin' madman but get all the hearts!
Okay, I chill now.
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ad6c35 No.8053
>>8051
Hope you don't mind those of us accelerating, just keeping the blood pumping.
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83b459 No.8054
>>8052
Well, if chillin' ain't required:
Highlander 2 is subtitled:
The Quickening.
If Podesta is scheduled to be picked up 11.3…
Might be a good time to start the 10 days of Darkness.
Get all the bad actors while they're acting to do something against the elections.
And don't forget, 2 rallies, each day, Nov 3rd and 4th.
That's lots of insulated, secure airtime on AF1, especially on the 3rd from D.C. to Montana to Florida.
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83b459 No.8055
>>8053
"The Other"… or maybe M… that you?
I remember chatting in the open waters about pokin' VQC to bring him back to wrap this up while ago.
Timing… timing…
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83b459 No.8056
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83b459 No.8057
>>8056
Granted… dimension bending…
Also a Villa of Mysteries reference?
"What really made Vesuvius explode? Did something go wrong in the Villa of Mysteries?"
https://www.archaeology.org/issues/124-1403/features/1813-pompeii-saving-the-villa-of-the-mysteries
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4c8c72 No.8058
>>8040
Just… something with staircase based jumps. Work in progress
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83b459 No.8059
YouTube embed. Click thumbnail to play. ALSO THIS!
"Blackout in the Red Room" by Love/Hate
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83b459 No.8060
Props to >>8058 for catching this
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83b459 No.8061
>>8047
Old School
"The Keystone is the Podesta Brothers."
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8b4129 No.8062
Before I take a break properly I suppose I should apologize for getting angry and calling you all lazy pricks. That's quite obviously not true. I stand by most of the rest of what I said, but it's inconsequential at this point, so I promise I won't mention it again. All I'll say is that >>7999 was pretty unnecessary.
>>8048
Would you mind responding to this (or telling me you aren't going to respond)? >>7986 The red text was just to get your attention since you miss questions semi-often (whether intentional or not).
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8b4129 No.8063
One last thing: based on >>8040 this, when you take the cells in (e,1) and (-f,1) where the two x values add together to make na, b-a in the (-f,1) cell is na+3 and b-a in the (e,1) cell is na+1. This is only tested on odd na so far.
Here are some test cases:
Find the element/cell where the x is equal to one of the staircase numbers for na/(n-1)a
(30:1:6) = {30:1:75:10:65:87} f=-121
(-17:1:6) = {-17:1:63:11:52:76} e=108
na=65 (so where x=32 and 33)
(30,1,17) = (30:1:559:32:527:593} f=-1089
(-17,1,17) = (-17:1:569:33:536:604} e=1120
b-a=604-536=68, b-a=593-527=66, na=65
(13:7:7) = {13:7:26:13:13:53} f=-40
(-40:6:8) = {-40:6:27:14:13:53} e=13
na=91 (so 45+46)
(13,1,23) = {13:1:1064:45:1019:1111} f=-2116
(-40,1,24) = {-40:1:1084:46:1038:1132} e=2127
b-a=1132-1038=94, b-a=1111-1019=92, na=91
(13:13:7) = {13:13:20:13:7:59} f=-28
(-28:12:8) = {-28:12:21:14:7:59} e=13
na=91
(13,1,23) = {13:1:1064:45:1019:1111} f=-2116
(-28,1,24) = {-28:1:1090:46:1044:1138} f=2151
94, 92, 91
(69:5:10) = {69:5:62:19:43:91} f=-56
(-56:4:11) = {-56:4:63:20:43:91} e=69
na=215 (107, 108)
(69,1,54) = {69:1:5866:107:5759:5975} f=-11664
(-56,1,55) = {-56:1:5912:108:5804:6022} f=11767
218, 216, 215
It might be useful to look into d[t]-d and a[t]-a in these cells, as well as comparing them to the cells where c*BigN and c*shadowN show up in (e,1) and (-f,1), and where x=f-1.
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b129f9 No.8065
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b129f9 No.8066
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b129f9 No.8067
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b129f9 No.8068
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b129f9 No.8069
bcbb19fc1667fcda9370c0d09a7f7f02
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8b4129 No.8070
Man, I've been angry for a while, huh? I've just been reading through older things. I'm really sorry everyone. I've had a shitty year and I didn't realize I was taking it out on you guys. This is the last I'll post about this whole thing, I swear. Don't mind me. Back to math.
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83b459 No.8071
>>8070
Huzzah!
Welcome back to The Wagon!
No fallin' off this time. ;)
And here, to make it like the comfy good ol' days… here's a Hitler.
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83b459 No.8072
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83b459 No.8073
From an anon in the open waters:
"check this out anons..might be relevant?
At the start of the summer term at Meadowbank School for Girls, a prestigious prep school in England, there is no reason for Miss Bulstrode, the popular but aging headmistress, to believe that the challenges facing her will be more than the occasional irate or inebriated parent. She scarcely listens when Mrs Upjohn, a parent, recognizes someone that she sees from her wartime days in the intelligence service. But there is a killer at the school who does not wait long to strike."
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a26807 No.8074
>>8070
Stay strong.
You're a good person and super smart.
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83b459 No.8075
>>8074
I concur!
Also… going back through the trips? kek
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a26807 No.8076
>>7986
The n0 base is a way to calculate through iterations the correct value of n or n-1. The iterations required are no bigger in complexity than Big Oh for the root of c.
Well done with the patterns.
It will happen when you come back to it.
From nowhere, in a moment when you decide not to give up.
Never give up.
I expect there is a very good reason why you were chosen to bring this to the world. That is why you are doing the pattern heavy lifting.
The patterns will give you a lookup.
When you see it, you won't unsee it.
I believe in you 100%
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a26807 No.8077
>>8075
What a year.
What a timeline.
Going to need a vacation before the Spring!
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83b459 No.8078
>>8077
You mean like Hawaii?
The parade got moved to next year…
Still planning on coming?
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0a3773 No.8079
>>8076
Hello VQC! Nice to see you.
The n0 base and triangle staircase numbers are derived from f, so they scale with every c value, correct?
On another thought: For the grid shortcut, does our program/algorithm need to be able to generate the elements surrounding the na transform in e,1 and -f,1?? The na transform lands us right in between (an) and (bn) in e,1 and a(n-1) and b(n-1) in -f,1. The movement from the na transform to the correct (an) and (bn) t or x values is very similar to the formula you described in your IP hopping post >>8040. The movement to (an) and (bn) is definitely two adjacent staircase numbers, and for a(n-1) and b(n-1) it happens as well. For c145 those numbers are 2 and 3 in e,1.
>To find the staircase numbers for an odd value, we add one to the value then divide it by two. Then the number is equal to the result added to the result minus one. Calculating this for the number we started with, would make two familiar values. Adding two side by side (t aligned) x values in e,1 and -f,1 would also make a staircase number.
>When na is odd, what do you do to find an identifier for the element where the x is equal to one of the staircase numbers for na? And if na is even, for n-1?
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566843 No.8080
>>8077
Hey VQC. Huge fan
Should I keep doing the grid stuff I'm doing?
>>8039
>>7886
I can look further into the factoring method if we should be doing that. I think there is a lot to be learned from these grids and if its as versatile as you say then it could be useful. On the otherhand the first discovery might be so mindblowing that anything else we do to utilize the grid would be trivial. I don't want to be wasting time.
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83b459 No.8081
>>8077
>>8060
>>8045
SO!
About that T-24hr….
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83b459 No.8082
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2344ac No.8083
So… what are your thoughts on how The Grid relates to RSA?
:
RSA revolves around Eulers PHI function, phi(N), pic related
phi has all primes on its diagonal and a fractal pattern inside a triangle
Our c is somewhere in the fractal, related to a,b who are predictably on the diagonal
Every point in a fractal is self-similiar
We are trying to find a pattern that ties our c to all its self-similiar points in the fractal
a and b are hidden in the pattern
Something about triangles, squares and fractals?
The Grid reverses the operation
It starts with some input 'c' and applies a square pattern on phi untill perfect squares(primes) are found???
Diagonals of prime squares?
The Grid is built for a specific version of RSA, specific constants
It might be easier to concentrate all our efforts on one specific path if we discuss how we SEE the problem.
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d1982e No.8084
>>8083
So we have our fractal, finally. I've been wondering about it.
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1ac2fe No.8085
Row operations on an augmented matrix result in an equivalent system of equations
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d02d29 No.8087
>>8086
is there a board that I could upload the .py to? Im still getting 100% accuracy, its fast too.
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b129f9 No.8088
>>8087
>>8086
All this is is a brute force algorithm that tests every square above d^2. Accuracy isn't the problem, efficiency is.
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abe23c No.8089
I was playing around with the Euler Totient. Based on the triangle from >>8083 I wanted to see how it looked like as a square. Not sure if this is the fractal we're looking for, but never the less it looks quite pleasing. You can see how there are squares and triangles pretty much everywhere inside of it. I really don't think this is where we are moving with regards to our fractal, but it was fun reading about the function and playing a bit with it.
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d02d29 No.8090
>>8088
I guess you are right. oh well
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b129f9 No.8091
>>7707
>>7706
>>7705
>>7704
Exponent vectors would explain this in a simpler way. I'll reformulate later
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4bf535 No.8093
//fractal patterns in prime distribution
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83b459 No.8094
>>8093
Hello coinkydinkle first time poster anon!
Welcome to our corner of the circle.
Please, check out the other topics in the catalog and remember…
Math is only EVERYTHING; so don't fuck up.
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b129f9 No.8095
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b129f9 No.8099
fractals:
Mandelbrot: recurse over f(z) = z^2 + c over and over for random complex points and color them based on whether they stay bounded or tend to infinity
Remainder tree: recursively calculate c = d^2 + e
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b129f9 No.8100
fractals and nature. viewed this way we see the pattern of a a tree stump
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d29b3e No.8101
All your base are belong to us
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b129f9 No.8102
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abe23c No.8103
I feel like an idiot again, it seems like every time I "get" part of what we do I end up feeling like an idiot.
Anyways, the smooth numbers are (a - 1)*(b - 1)/2. That is, BigN - n = (a - 1)(b - 1)/2.
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83b459 No.8104
>>8103
The fact that you get any of this makes you more intelligent than most of the human population.
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3412ba No.8105
>>8103
Walking into the unknown is a rarity and everyone has the capability to do genius things.
Trust someone who stared at this for seven years.
You can do this.
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83b459 No.8106
>>8105
What a coincidence, one of a long string of first time poster anons!
So did that one guy!
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0868a8 No.8109
>>8101
Hello Senpai, nice to see you!
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e12188 No.8110
n values for the first 28 triangle numbers (from ColumnKeys function)
T(1) = n/a
T(2) = [1]
T(3) = n/a
T(4) = n/a
T(5) = [1, 5]
T(6) = [1, 7]
T(7) = [3]
T(8) = [4]
T(9) = [1, 3, 17]
T(10) = [1, 21]
T(11) = n/a
T(12) = n/a
T(13) = [1, 37]
T(14) = [1, 3, 9, 43]
T(15) = [1, 3, 7, 21]
T(16) = [8, 24]
T(17) = [1, 15, 65]
T(18) = [1, 17, 73]
T(19) = n/a
T(20) = n/a
T(21) = [1, 5, 25, 101]
T(22) = [2, 112]
T(23) = [10, 54]
T(24) = [3, 11, 59]
T(25) = [1, 17, 145]
T(26) = [2, 6, 42, 158]
T(27) = n/a
T(28) = n/a
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e12188 No.8111
>>7007
It returns pairs of n and n-1.
For example, if we input -24, 1 it will return
[[4, 5], [60, 61]]
since -f and e combined make the columns unique to c. Can this function be reconstructed from a description of how it behaves?
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e12188 No.8112
This is a diagonal, since it describes pairs of n that are one (row) apart. How do column -f and e when used together at once materialize the solution, since the diagonal and the patterns they make when used in tandem are unique to c?
It will all make sense in hindsight.
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83b459 No.8113
>>8112
I do my darnedest to remind the Nerds to post here, I swear.
Side note, if there is "space between squares", is there space between trangles?
What about space between Trangles AND Squars?
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2bd1d5 No.8114
https:// curvaturasvariantes.com/2018/06/12/galois-theory-hodge-conjecture-and-riemann-hypothesis-visual-geometric-investigations/
https:// curvaturasvariantes.com/2018/05/25/about-prime-numbers-symmetries/
<3
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83b459 No.8115
>>8114
Oooooh, a third one!
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b129f9 No.8116
I didn't find i[t], i[t] found me!
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b129f9 No.8117
Math without art - no such thing!
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b129f9 No.8118
"I knew this would make a swastika eventually" v2
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0c3c6f No.8119
1) Draw a circle.
2) Pick a c value which is the sum of squares (c values where e=1,4,9,16,25..)
3) Set the radius of the circle equal to the square root of c (this calculation includes decimals).
4) Every integer point the circle passes through will be a valid sum of squares that makes c. (e.g the circle for sqrt(145) passes through (12,1) and 145 = 12^2 + 1^2)
A c example equal to the sum of squares was chosen for a reason.
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0c3c6f No.8120
This is because the formula for a circle reduces to the sum of squares when the circle's centerpoint exists at the origin (a and b in the formula = 0). The cell where e and n = 0 also functions as an origin.
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0c3c6f No.8121
https:// en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares
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83b459 No.8122
>>8121
>>8120
>>8119
I think the Nerds might have lives or something, but I'm here.
Please continue!
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83b459 No.8123
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566843 No.8125
>>8119
>>8120
>>8121
https://www.m ath.hmc.edu/funfacts/ffiles/20008.5.shtml
>Which whole numbers are expressible as sums of two (integer) squares?
>Here's a theorem that completely answers the question, due to Fermat:
>A number N is expressible as a sum of 2 squares if and only if in the prime factorization of N, every prime of the form (4k+3) occurs an even number of times!
>Examples: 245 = 5*7*7. The only prime of the form 4k+3 is 7, and it appears twice. So it should be possible to write 245 as a sum of 2 squares (in fact, try the squares of 14 and 7). But because 7 appears only once in 42=2*3*7, it is impossible to write 42 as the sum of two squares.
>A corollary of this fact is that every prime of the form (4k+1) can be written as the sum of two squares.
So since 145 is a sum of 2 squares so 145 = 4k+1 for k=36 = 12*12 + 1*1
I think I learned in number theory way back when a way to get these squares for a number. Not sure though.
We know for a fact that it is coprime, so there are two factors. If one is equal to 4k+3, then the other must also be equal to 4k+3 for different k's because it can be written as a sum of two squares. If one factor is equal to 4k+1, then the other must also, because 0 is for this sake an even number.
So if a number is a sum of two squares, it is either
c = (4k+1)(4j+1) or (4k+3)(4j+3) for some j and some k
Lets look at the formula (d+n) = (b+a)/2 and (x+n) = (b-a)/2,
Suppose a=4k+1 b=4j+1,
d+n = (4j+1 + (4k+1))/2 = (4j + 4k + 2)/2 = 2(j+k) + 1
x+n = (4j+1 - (4k+1))/2 = (4j+1 - 4k - 1)/2 = 2(j-k)
for c=145 = 4(36) + 1
a = 5 = 4(1) + 1 ==> k=1
b = 29 = 4(7) + 1 ==> j=7
(d+n) = 2(j+k)+1 = 2(7+1)+1 =17
(x+n) = 2(j-k) = 2(7-1) = 12
Now suppose a=4k+3 and b=4j+3
d+n = (4j+3 + (4k+3))/2 = (4(j+k) + 6) / 2 = 2(j+k) + 3
x+n = (4j+3 - (4k+3))/2 = (4(j-k))/2 = 2(j-k)
For c = 253 = 4(63) + 1
a = 11 = 4(2) + 3 ==> k = 2
b = 23 = 4(5) + 3 ==> j = 5
(d+n) = 2(j+k) + 3 = 2(2+5) + 3 = 17
(x+n) = 2(j-k) = 2(5-2) = 6
This is super cool because every number that is the sum of two squares has (x+n) = 2(j-k).
Its almost as if it maps all the numbers from 2k+1 to 4k+1 in such a way.
Like for the 145 example,
a = 4(1) + 1
b = 4(7) + 1
Call the 1 and 7 the core components of the number. You can add and subtract these, and when you do you generate an odd and an even number
For these situations d+n is the odd component. I'd imagine when c=4k+3 that is the reverse but same type of stuff.
(d+n) = 2(7+1) + 1 = 17
(x+n) = 2(7-1) = 12
The same type of thing holds for c=253, but the leaf (odd number) is 3 instead of 1
a = 4(2) + 3
b = 4(5) + 3
(d+n) = 2(5+2) + 3 = 17
(x+n) = 2(5-2) = 6
Getting anywhere??
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566843 No.8127
>>8125
If we look in here
Pic 1 can show you a few things. The core element of b is always the sum of the core for d+n and x+n. Also the core for a is always the difference of d+n and x+n.
Whats interesting is that for these 4 numbers (a,b,d+n,x+n), the pattern always holds no matter what base you're in. Also another thing is that the leaf numbers of d+n and x+n always add up to the leaf number of b.
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b129f9 No.8128
>>8127
Please make your posts clearer. You haven't explained to anyone else what leaf numbers exactly are or what a "core" element is, not to mention your functions
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566843 No.8129
>>8128
If a number c is a sum of two squares, then it is of the form 4k+1. Here, the 4 is the multiplier, the k would be the core and the 1 would be the leaf. I'm proposing that the multiplier can be any power of 2 and the k can be any number and then the leaf would then have to be a number less than the multiplier.
If a square c is of the form 4k+1, then according to the link I posted it's prime factorization must have primes of the form 4k+3 occurring an even number of times [here, 4 would be multiplier, k core and 3 leaf]. Since we know c is coprime (2 prime factors) and that they are odd, the only two types of numbers they can be are 4k+1 and 4k+3. Since the factors of the type 4k+3 must occur an even number of times and there are only 2 factors, the even numbers are either 2 or 0, so either both factors are 4k+3 for different k's or they are both 4k+1 for different k's. Keep in mind, this is only for c = 4k+1.
Knowing this, I algebraically looked into the d+n and x+n values in this format through the formulas:
d+n = (b+a)/2
x+n = (b-a)/2
I found that if
a = (4)(k) + L
b = (4)(j) + L
For L=1 or 3 and since b>a, j>k
Then you can find the d+n and x+n values like this
d+n = (2)(j+k) + L
x+n = 2(j-k)
So instead of doing all the calculations you could look at it like this:
>Divide the multiplier by two
>Take sum and difference of core elements
>Decrement L by one for the difference
I'm thinking we might be able to take this formula and do other things with it, but I am still looking. For instance what if we increase all the powers? Then does the function map to a different calculation? If you increase the multiplier to greater than the initial number, then the entire number would just be a leaf because the core would be 0. Obviously every single number can be written as another number.
15 = 16(0) + 15 = 8(1) + 7 = 4*(3) + 3 = 2*(7) + 1 = 1*(15) + 0
Look here, the leaf goes 15->7->3->1->0
and the core goes 0->1->3->7->15
They reverse but the power decreases.
I think we should look into this
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566843 No.8130
Another thing we can use this type of stuff for is Legendre Symbols.
The legendre symbol (I'll denote it as (a//p)) is:
0 if a is divisible by p
1 if a is a quadratic residue mod p
-1 if a is not a quadratic residue mod p
If a IS a quadratic residue mod p, then there exists a number M where M*M - a = k*p for some k.
Or the square of M is a units more than a multiple of p.
We could make a a negative number, which would switch the equation to M*M + a = k*p.
Then its a square plus a number equals a product of 2 numbers (one of which is necessarily prime), which is our entire problem.
If you look further into these numbers, you'll see things where this type of math is used.
If you let a=-1, then the legendre symbol (a//p) can be calculated directly through this calculation:
(a//p) = 1 if p = 4k+1
(a//p) = 3 if p = 4k+3
If you let a=-2, then
(a//p) = 1 if p = 8k + 1 or 8k + 3
(a//p) = -1 if p = 8k + 5 or 8k + 7
If you let a=-3, then
(a//p) = 1 if p = 12k + 1 or 12k + 7
(a//p) = -1 if p = 12k + 5 or 12k + 11 (3 or 9 dont seem to show up)
a = -4
(a//p) = 1 if p = 8k + 1 or 8k + 5
(a//p) = -1 if p = 8k + 3 or 8k + 7
a = -5
(a//p) = 1 if p = 20k + {1, 3, 5, 7, 9}
(a//p) = -1 if p = 20k + {11, 13, 17, 19} (15 doesnt seem to show up)
a = -6
(a//p) = 1 if p = 24k + {1, 5, 7, 11}
(a//p) = -1 if p = 24k + {13, 17, 19, 23}
Basically it looks like you can check divisibility without actually calculating anything except the mod of 4 * the number. The -4 case is unique though I'll look more into that. There may be numbers missing from these but generally speaking the ideas is right. I'll write a script later to more easily calculate this stuff and verify it.
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e42aae No.8131
>>7990
>c=i^2+ij-ji-j^2
Thanks for this perspective.
Using ij = (d+n)(x+n) as the mid-point between the large and small squares, went looking for a way to either directly calculate a factor or reduce the iterative search space for finding the solution small square.
Pics attached explore the ij = (d+n)(x+n) "middle" rectangle for various test cases, and includes a square/triangle breakdown for c6107 as an example of how factors could be extracted from this middle area.
The analysis is based on the formulas (DPN - ij) and (ij - XPN), where DPN = (d+n)^2 and XPN = (x+n)^2.
Reason for this approach is that the a[t] values from the na transform (-f,1) and (e,1) starting records are either very close to or an exact match with the (ij - XPN) or (DPN - ij) values. (see c145 as an example).
The "gcd" and "sqrt" columns provide an alterative way to find the solution "a" values and are calculated as:
gcd = gcd(c,(ij - XPN))
sqrt = sqrt((DPN - ij) - (ij - XPN))
Both formulas return the solution "a" value, except for c363 where the gcd result is a^2.
Additional testing has found that the following gcd formulas also work:
a = gcd(c,(ij - XPN))
a = gcd(c,(DPN - ij))
b = gcd(c,(ij + XPN))
b = gcd(c,(DPN + ij))
Furthermore, the sqrt formula (DPN - ij) - (ij - XPN) can be simplified to aa=(d-x)^2. Indicating again the need to find the correct "x" value.
One way to take advantage of these formulas would be to somehow calculate or iterate to the (ij - XPN) value. The last 2 columns using the min_a variable were an attempt to isolate and understand these gaps (2d+1 keeps appearing).
Alternatively, this analysis may lead to an improved iterative search estimated x+n starting position based on the na (e,1) a[t] value.
For c6107, that starting position would be x+n = sqrt(2976) = 54, and reduces the iterative search space by half (see pic attached).
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83b459 No.8133
>>8131
>>8132
Posting the same thing twice doesn't earn you double EXP.
You've already gained all the power you can from that node.
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e42aae No.8134
>>8133
Weird "flood detected" and "alacrity" errors during post.
Duplicate deleted.
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e42aae No.8135
>>8110
Pic attached is for triangle numbers between 500 and 530 and includes variables previously hinted for the ColumnKeys function.
The n/a columns represent c mod 4 = 2 numbers that don't exist in the grid. These require c/2 to find valid entries.
n values of 22 and 23 have been highlighted to show perhaps similar behaviors that needs to be explored further.
Interesting that in some cases the sqrt(2d), sqrt(f), or sqrt(e) values come very close to a correct n.
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296e69 No.8136
Hello Lads! I'm reviewing crumbs looking for traction. We haven't figured out yet how 2d and f limit the possible (n-1) values. Based on VQC's instructions in the attached pic, we split off one (n-1) value in the x+n square formula. The formula looks like this after being modified:
nn+(2d-1)(n-1)+f+(n-1)-1
I was just thinking about a new way to examine the mods.
Let’s take familiar c values, and break them down in two ways:
Method 1: Using the (f-1)div 8 method, showing all mods as well.
Then let’s have columns with 2d-1 and f for that c.
Method 2:
Then let’s have columns breaking down each part of nn+(2d-1)+f-1 into div 8 and mod 8.
Goal is to find the connection between 2d, f, and the n or (n-1) values that give a correct lock for the x+n square. We need to see how EVERY piece contributes to completing the x+n square.
To make it work, I think we need medium/large c values, like in the millions range.
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85b403 No.8137
https:// en.wikipedia.org/wiki/Non-Euclidean_geometry
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83b459 No.8138
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85b403 No.8139
https:// en.wikipedia.org/wiki/Fractal_compression
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85b403 No.8141
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85b403 No.8142
https:// math.stackexchange.com/questions/1579998/fractals-using-just-modulo-operation
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85b403 No.8143
Hint:
A factor is immediately weeded out by the VQC for c=15 because gcd(d,e) != 0
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85b403 No.8144
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3416be No.8145
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83b459 No.8146
>>8145
Golly… it's as if the space between the squares is like… a constant… or something.
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83b459 No.8147
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3416be No.8148
>>8145
>>8146
Bigger. Longer. a jumps by 191 each frame, now in mp4 for moar better
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83b459 No.8150
https://en.wikipedia.org/wiki/Computability_theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory.
Basic questions addressed by recursion theory include:
What does it mean for a function on the natural numbers to be computable?
How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?
https://en.wikipedia.org/wiki/Recursion
Recursion occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no loop or infinite chain of references can occur.
https://en.wikipedia.org/wiki/Fractal
In mathematics, a fractal is a detailed, recursive, and infinitely self-similar mathematical set whose Hausdorff dimension strictly exceeds its topological dimension.
https://en.wikipedia.org/wiki/Multifractal_system
A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed.
https://en.wikipedia.org/wiki/Fractal_canopy
In geometry, fractal canopies are one of the easiest-to-create types of fractals. They are created by splitting a line segment into two smaller segments at the end, and then splitting the two smaller segments and as well, and so on, infinitely.
(See Pics)
https://en.wikipedia.org/wiki/Orbit_trap
In mathematics, an orbit trap is a method of colouring fractal images based upon how close an iterative function, used to create the fractal, approaches a geometric shape, called a "trap".
(Pic 3)
https://en.wikipedia.org/wiki/Pickover_stalk
Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry.[1] They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. An "epsilon cross" is a cross-shaped orbit trap.
(Pic 4)
https://en.wikipedia.org/wiki/Fractal_dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
https://en.wikipedia.org/wiki/N-flake
An n-flake, polyflake, or Sierpinski n-gon,[1]:1 is a fractal constructed starting from an n-gon. This n-gon is replaced by a flake of smaller n-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center. This process is repeated recursively to result in the fractal. Typically, there is also the restriction that the n-gons must touch yet not overlap.
(Pic 5)
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3416be No.8152
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a2f757 No.8157
Wrong answers destructively interfere.
Right answers consecutively interfere.
QFT = Column Zero
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43f2b8 No.8160
>>8157
I think I'm on board, at least partially. I just got to start exploring this though, so hold your thoughts a bit while I try and catch up.
I'm still not entirely on board with the M-function, mostly in the sense of using it with regards to the records, but like I said I'm exploring it and thinking about it. I'm getting now that with the QFT (Column 0, row 1 (?)) we should be able to find the period of the number we're after. This should allow us to compute Shor's algorithm.
In >>8148 is the fractal overlayed, as in two pictures one with a moving M over another stationary M?
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43f2b8 No.8161
>>8157
The images are something I made today, so they might not be accurate, but the first one should be M moving 2 times pr. frame while the second one is moving 8 times pr. frame, if I'm on board with the "jumping". However, neither are tied to a record, they're generated using M with x, y and offsets. (I went through a few tests before I figured out how to emulate the movement compared to the videoes you posted).
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43f2b8 No.8162
>>8161
Something interesting to note is how you can clearly see squares appear on the diagonal as the "beams" split.
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e42aae No.8163
>>8135
Integrated the gcd(d,e) and remainder tree into previous work on the ColumnKeys function, and found a number of cases where "e" represents either a valid x or x+n.
Pic attached is for odd c values between 10000 and 12500 where e mod 4 = 3.
In some cases, a factor can be found simply by a = gcd(d,e) != 1.
In others, the "x in tree" column indicates where in the remainder tree a matching x or x+n value from a factor record is found:
(e x1) indicates x=e at the first branch of the tree.
(e xpn2) indicates x+n=e at the second branch of the tree.
For c12247, as an example, the factor record is found at x+n=e=147.
For c5247, where there are multiple factors, interesting that factor records appear both where x=e and x+n=e.
Not yet sure what family of numbers this x=e and x+n=e can be used to factor.
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e42aae No.8164
>>8163
Some additional proof of concept tests on the x=e and x+n=e idea.
These examples are for all odd c values between 9000000000 and 9000100000.
x=e tests are resolved simply by a=d-x, and c % a = 0. Records are created by e,d, and abs(a).
x+n=e tests use the n0 and rm2dnm1 triangle solution from the (x+n)(x+n) square. Records are then created by e,n,d.
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da1222 No.8165
What is the one VQC hint that not a single person investigated or posted about?
That is the solution.
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da1222 No.8166
A hint designed to be overlooked.
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83b459 No.8167
>>8166
>>8165
Can I has context?
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8b4129 No.8168
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83b459 No.8169
>>8166
>>8165
>>8167
"The m'lady of the group" suggests:
"Why is e=1 in the first example given?"
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2344ac No.8170
for a moment consider every digit in a base a unique component
multiplication a composition and division decomposition of a number
sum, as all possible linear combinations of unique components to construct a number
base10,mod9:
-791=7+9+1=17=1+7=16+1=91+7=8
-791=16mod9+1mod9=91mod9+7mod9=8mod9=8
-135727=1+3+5+7+2+7=13+57+27=135+727=75+13+27=123+577=7
-478=1
if a in base10 then sum_digits(a)=amod9
whole part of division by 9 is number of overflows in the algorithm
base16,mod15:
-791=0x317=0x3+0x1+0x7=0xB=0x31+0x7=0x17+0x3=0x38 →convert to base10,mod9→0xB=11->0x11->17=8
-791=0x317=0x31mod15+0x7mod15=0xB
the result in base16 is actually a direct result in base10: 791/15=52+11
-135727=0x02122F=0x0+0x2+0x1+0x2+0x2+0xF=0x16=0x000007=0x02+0x2F+0x12→convert to base10,mod9→0x7=7->0x7->7=7
-478=0x01DE=0x0+0x1+0xD+0xE=0x01+0xDE=0x1D+0x0E=0x001C=0x000D →convert to base10,mod9→0xD=13->0x13->19=1
the result: 478/15=31+13
how to do division using only addition?
c=a/b
a in base10
convert a to base(b+1)
sum the digits arbitrarily
when sum>b, ovf++;
sum=remainder
ovf=whole part
once you have the remainder of a for one base, you can easily convert between bases and get remainder for other divisions
now imagine you have a number c that is 100 digits long in base10
in base100 the digit itself is the remainder, ovf=0
idk,maybe… will try to write up a script later for arbitrary bases to see what we get.
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4b92c9 No.8171
Anons.
I took a job in Amsterdam to have as much time to monitor threads as possible.
I know there are questions.
I know you are waiting.
I have questions too.
Unfortunately, recovery isn't working here in Amsterdam and I am dying of alcoholism.
Through self-pity at my own hands or liver failure, my time is almost up.
For those that also love POTUS, please don't ever give up.
The Twelve Steps are the solution for bEtter meN.
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b129f9 No.8172
>>8171
I don't believe you! Prove identity.
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b129f9 No.8173
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83b459 No.8174
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566843 No.8175
>>8171
>We admitted we were powerless over our addiction - that our lives had become unmanageable.
>Came to believe that a [Power] [greater than] ourselves [c]ould restore us to sanity.
>Made a decision to turn our will and our lives over to the care of [God] as we understood [God].
>Made a searching and fearless moral inventory of [ourselves].
>Admitted to [God], to ourselves and to another human being the exact nature of our [wrongs]
>Were entirely ready to have G[o]d remove all these [defects] of [c]haracter.
>Humbly asked God to [remove] our [shortcomings].
>Made a list of all [persons] we had harmed, and became willing to make [amends] to them all.
>Made direct amends to such [people] wherever possible, except when to do so would [injure] them or others.
>[Continued] to take personal inventory and when we were wrong promptly admitted it.
>Sought through prayer and meditation to improve our conscious contact with God as we understood God, praying only for knowledge of God's will for us and the power to carry that out.
>Having had a spiritual awakening as the result of these steps, we tried to carry this message to other addicts, and to practice these principles in all our affairs.
>The Twelve Steps are the solution for bEtter meN.
EN is the obvious clue.
These steps above could refer to this puzzle?
Lets say 'we' are the number c.
>Came to believe that a Power greater than ourselves could restore us to sanity.
Power greater than c so
(d+1)^2 > dd+e
c^2 > c
Either of these could potentially be leads. I think its c^2 cuz VQC said that before it was important
>Made a decision to turn our will and our lives over to the care of God as we understood God.
If I had to guess what 'God' is in this context I'd say it is the number 1. Thats what a lot of people say it is anyway
Maybe thats the (e,1) row and use what we know about that row to do stuff with the record
>Made a searching and fearless moral inventory of ourselves.
This could be some tree generation with the dd+e trees.
>Admitted to God, to ourselves and to another human being the exact nature of our wrongs.
I'd say that since we have dd+e e has always seemed to be a little extra piece that we don't need. I think maybe then we could collect the extra parts from each division. The sum of those could be the 'defects of character' in that they aren't perfect squares.
>Were entirely ready to have God remove all these defects of character.
>Humbly asked God to remove our shortcomings.
c - (sum of all minor e values) = something
>Made a list of all persons we had harmed, and became willing to make amends to them all.
So somehow we are going to be using numbers along the line, I think for this it would mean add a certain amount to these values you've seen along the way. I'd say its the numbers in the tree.
>Made direct amends to such people wherever possible, except when to do so would injure them or others.
Add the numbers to the cells unless it would invalidate a cell
>Continued to take personal inventory and when we were wrong promptly admitted it.
This implies some sort of while loop I think
>Sought through prayer and meditation to improve our conscious contact with God as we understood God, praying only for knowledge of God's will for us and the power to carry that out.
Something something I don't know maybe trust row n=1
>Having had a spiritual awakening as the result of these steps, we tried to carry this message to other addicts, and to practice these principles in all our affairs.
Use this algorithm to do everything because its super cool
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4b92c9 No.8176
The whole point of the VQC is to create a lookup.
Equivalent to user friendly quantum fast Fourier transform.
The patterns will show you how.
Last post.
Pwds:
matariki
ja5p3rm00
th33nd
All these moments will be lost, like tears in rain.
Time to die.
No more secrets.
Set free.
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83b459 No.8179
>>8176
Verified…
Interdasting development…
So… no more character named Chris… but Chris was never really your name to begin with.
Does this mean "Last post as VQC" or "Last post anywhere, even as anon"?
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b129f9 No.8181
But just so you know. I tried this before. People don't die of liver failure.
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b129f9 No.8182
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b129f9 No.8184
Correction - natural logarithms are logarithms calculated with e as the base
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b129f9 No.8185
>>8176
Isn't it funny how you can post "final piece" and then "O log t where t is the length of c in bits" immediately afterwards and then nobody analyzes it for months
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83b459 No.8186
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8b4129 No.8188
>>8185
The only thing I ever took from that was that maybe you used the letter t because it's equivalent to the index variable t. But that's O(1). I never looked into it so I'll do that now.
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83b459 No.8189
YouTube embed. Click thumbnail to play. >>8188
Not sure I follow on the "figured out"… I thought everyone knew that was the narrative…
Anyway, before things go potentially haywire, would you be a doll and use your magical powers of being BO, filter for trips, and get screenshots for us?
Just to have a solid record before things go potentially haywire due to trip release.
Thank you!!! ^_^
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b129f9 No.8190
>>8188
I'm not Chris. He compromised his tripcodes.
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83b459 No.8191
YouTube embed. Click thumbnail to play. >>8188
>>8189
I was misreading. Gotcha gotcha.
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8b4129 No.8192
>>8189
>>8190
There's not a lot screenshots are going to help with that.
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83b459 No.8193
>>8192
How do the BO and BV's over on the Q boards do it? Maybe there's a view change?
They point out the shills by what seems like viewing the posts on a grid and then screenshotting how ever many it takes.
Or pulling the whole page in one image directly, and I could chop it up from there.
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8b4129 No.8194
>>8193
That's only useful when it's happening actively and throughout multiple threads. Since VQC keeps IP hopping, without trips, there's no way to prove any of the posts in this thread other than the ones with his trip before he posted those passwords are actually him. 90 days from now, there'll be nothing tying him to any of the IDs in this thread, since the hashes will reset. I'm not sure what you actually wanted to achieve with me screenshotting his posting history.
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b129f9 No.8195
>>8194
If you realized something about the post you just made, keep it a secret.
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8b4129 No.8196
>>8185
At risk of coming across as frustrated (my intention with this is to understand your perspective, not to figure out how to use the VQC), surely you realize that since you figured out something so monumentally unheard of, and since you're posting about it so cryptically, obviously we're not going to figure out what everything you post means, right? As much as you're probably completely sure you've given us enough information to solve this, and that connecting two tiny, obvious dots would solve it, O(log t) where t is the length of c in bits is extremely vague.
I hope you've at least got the will to get out of Amsterdam instead of giving up.
>>8195
Wut
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b129f9 No.8197
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83b459 No.8198
>>8196
In case of any discord and because we were gonna make a thread about it/maps.
Like…
Maths vs Ayy LMAO vs Spacetime/Physics vs Bantz
That sorta thing. Like… think of this as a marker so we're consolidating what we have up until now.
And if you can filter for JUST his various trips or if his ip hashes remained constant per trip (hide anything not already public), that'd be really helpful, if you can and don't mind.
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8b4129 No.8199
>>8197
Oh whoops. Isn't that ironic. You didn't answer the other reply.
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b129f9 No.8200
>>8199
The number line isn't a line. It looks more like a Mobius strip (much like the 8ch logo), with e and infinity on different sides of the same point.
0 doesn't exist - the remainder of taking everything away is Euler's number.
The remainder of taking everything away is e.
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8b4129 No.8201
>>8198
Pic related is all that's associated with that IP hash, so there you go.
>>8200
So what do we do with this information?
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b129f9 No.8202
The CMB (Cosmic Microwave Background) has a thermal black body spectrum at a temperature of 2.72548±0.00057 K.[4] (Wikipedia)
2.72548 plus/minus 0.00057
e=2.71828
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83b459 No.8203
>>8201
I meant literally all of them.
Be way easier if we could talk to you about this in a more conversational format
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b129f9 No.8204
>>8201
There is a connection between base, e (of c), Euler's number, d^2+e, O(log t where t=bitlength of c) hints
"This pattern GROWS in a certain way"
O notation is about how efficiencies grow
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8b4129 No.8205
>>8185
So if this was Jan then it isn't necessarily what the hint was about.
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8b4129 No.8206
>>8111
My point was that the comments didn't seem like they were from the same function.
>Can this function be reconstructed from a description of how it behaves?
Not if we don't know how to calculate n, no.
>>8144
>>8143
Jan, if you're still looking for a fractal, here's a potential end point.
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8b4129 No.8207
I found a hole in the whole “each pair of e and f only has one set of n and n-1 values” thing from >>8111 here.
>//given two columns, which values of n are separated by 1
That was the code comment. So the idea is that for your given semiprime c (which has a unique set of d, e and f), in that specific pair of e and f columns, there will only be two pairs of n and n-1 values (prime n and BigN). This isn’t true. Take 13*43=559, for example. e=30 and f=-17. Starting from n=1 (ignoring it though obviously), these are the n values that appear in the e=30 column:
3, 5, 11, 13, 15, 17, 23, 29, 31, 33, etc
These are the n-1 values that appear in the f=-17 column:
2, 4, 8, 13, 16, 17, 19, 26, 32, 34, etc
The valid pairs of n and n-1 are [3,2], [5,4], [17,16], [33,32] and so on. So there are actually probably infinite valid pairs. The only thing unique to [5,4], the correct one, in this case, is that there are two cells within these that share a d value. But that’s not what the comment said:
>//given two columns, which values of n are separated by 1
It doesn't say anything about d.
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09e44c No.8208
>>8176
>>8181
Hello V. You're not alone. Thank you for you. Thank you for all you've done and shared, your pattern is unique and the ripples will flow forever, no matter what and no matter when.
This work has generated some hope and faith in people and the future. More than you know.
Check in every day, and follow along, just can't fit in contributing atm so went to lurk mode.
Love to you.
No more secrets.
Victory in peace.
So much respect for all you fags.
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09e44c No.8209
>>8207 ty anon, for all the word and dedication.
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b129f9 No.8210
HookTube embed. Click on thumbnail to play. Disclaimer: this post and the subject matter and contents thereof - text, media, or otherwise - do not necessarily reflect the views of the 8kun administration.
Post last edited at
b129f9 No.8211
Good morning. Last night things were difficult and I did not react appropriately. I want to say that I am thankful to Chris for everything, for sharing all of these revelations and things which we know by faith are true. Before this, I was not good at math and had no way of approaching the subject, especially for special avenues like this one. But now I have been given one.
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b129f9 No.8212
We will solve this. The enumeration of all patterns given is almost complete. And when we do, the limits of the Virtual Quantum Computers we can create will be what we dream up. Extension to Discrete Logarithms will be swift ["The DLP can be thought of as a 2 dimensional version of the factoring problem."] Patterns in the Mandelbrot show that Devices which Calculate all Values exist in the realm of mathematics. Fractal image compression using exact self similarities - Image manipulation using universal self similarities [The Eye] - Engineering desktop cold fusion by a sonoluminescence feedback loop - Inverting Hash Functions [special type of value table]
The world will never be the same.
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8baa18 No.8213
"Algebraic operations can be done readily on the power series representation; for instance, Euler's formula [e] follows from Taylor series expansions for trigonometric and exponential functions. This result is of fundamental importance in such fields as harmonic analysis."
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8baa18 No.8214
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8baa18 No.8215
Euler's Factoring Method.
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8b4129 No.8216
>>8214
>>8213
>>8215
Hmm, I wonder who this is
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83b459 No.8217
YouTube embed. Click thumbnail to play. I miss Chris already.
all the feels
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9b63df No.8218
>>8176
I would like to say that it's sad to see you burn your verification like this, but let's be honest here; We recognize the lion by his claw.
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83b459 No.8219
>>8218
You tell 'em, clearly first time posting anon!
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4ac8ad No.8220
>>8219
I love you Topo, but it's just ISP here.
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7b4eb6 No.8222
>>8200
that's what I've been saying for months
fuckin MONTHS
Are you just parroting my theories from qresearch/vqc or are you confirming that I'm not actually crazy and that there's a method to my madness?
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7b4eb6 No.8223
^^^^
that's not angry, it's more of a sputtering guffaw
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83b459 No.8226
>>8221
Did you pre-plan an (e) into that because of American vs British spelling of "fair(e)"?
kek
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83b459 No.8230
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83b459 No.8231
>>8230
A thought…
"An Existential Proof for P=NP instead of a Constructive Proof… hmmm…."
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83b459 No.8233
>>8232
>say entreaties put feebly favour him, sufficient few pianoforte discovered uncommonly ask
Morning cousins amongst in mr weather do neither. Warmth object matter course active law spring six. Pursuit showing tedious unknown winding see had man add. And park eyes too more him. Simple excuse active had son wholly coming number add. Though all excuse ladies rather regard assure yet. If feelings so prospect no as raptures quitting.
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83b459 No.8235
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83b459 No.8237
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83b459 No.8241
>>8240
Nifty!
Whatcha do with whatdja wrote?
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ca2fe5 No.8248
It would be good to start studying soon.
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83b459 No.8249
AA… maybe you pop into the chat a lil more often for a bit…
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8b4129 No.8250
>>8249
I have a life outside of this board, gosh well, occasionally
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e42aae No.8251
Looked a bit deeper into Euler's totient function.
fi(c) is calculated as the number of values k between 1 and c where gcd(k,c) == 1.
fi(145) = 112
Fruitful discussion on the discord yielded some pretty incredible equations (courtesy of Jan) using fi:
145 = 5 x 29
112 = 4 x 28
fi(c) = (a − 1)(b − 1)
fi(c) = ab − a − b + 1
fi(c) = c − a − b + 1
a+b = c - fi(c) + 1
we know:
(a+b)/2 - d = n
a+b = 2(d+n)
Therefore, we can define d+n in terms of c and fi(c) as follows:
d+n = (c - fi(c) + 1) / 2
c145
(1,5,4) = {1:5:12:7:5:29} = 145; (d+n)=17
fi(145) = 112
d+n = (145 - 112 + 1) / 2 = 17
c6107
(23,36,24) = {23:36:78:47:31:197} = 6107; (d+n)=114
fi(6107) = 5880
d+n = (6107 - 5880 + 1) / 2 = 114
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e42aae No.8252
>>8251
Also found an alternate way to calculate n using fi using the (e,1) a[t] value from the na record.
n = a[t] - (fi(c)/2)
c6107
(e,1) na: {23:1:3053:77:2976:3132}
solution: {23:36:78:47:31:197}
fi(6107) = 5880
n = 2976 - (5880/2) = 2976 - 2940 = 36
c901
(e,1) na: {1:1:450:29:421:481}
solution: {1:5:30:13:17:53}
fi(901) = 832
n = 421 - (832/2) = 5
c34117
(e,1) na: {261:1:17058:183:16875:17243}
solution: {261:27:184:75:109:313}
fi(34117) = 33696
n = 16875 - (33696/2) = 27
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8b4129 No.8253
>>8251
(a-1)(b-1) = 2(BigN-n) as well.
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e42aae No.8254
>>8252
Pic attached is a revised columnkeys test incorporating the fi(c) calculation for odd c values between 6000 and 6500.
The formula posted previously, and shown in the last column, can be simplified to:
n = N - fi(c)/2
where N is from an entry c record, and n is in the prime solution record.
Reviewing the data, this n formula works where c is the product of 2 primes for both odd and even parities of n. See odd n c6019, c6023, c6031 and even n c6001, c6005, c6103, c6107 as examples.
When c is a prime number, the formula returns -(d-1) or -x (same value for an odd entry record). See c6007, c6011, c6029, etc.
Not quite sure what the return value means for c with many factors, but perhaps this is where the algorithm comes into play.
Based on this, it appears that a direct calculation is possible for the product of 2 primes - depending, of course, on a grid solution to the fi value for any c.
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b129f9 No.8255
>>8254
Because fi(c) = (N-n)/2
Hence, the connection with smooth numbers (and that connection to Shor period values) grows.
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b129f9 No.8256
>>8255
Correction:
fi(c) = 2(N-n)
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02d76c No.8257
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83b459 No.8258
YouTube embed. Click thumbnail to play. Disclaimer: this post and the subject matter and contents thereof - text, media, or otherwise - do not necessarily reflect the views of the 8kun administration.
cc56f4 No.8259
Hello everyone!
Well, I have all day off finally. Let's think and work as a team.
I'm reviewing all my notes, and reading through the Grid Patterns thread. >>6506
AA did a really nice job getting the crumbs all organized.
You guys were talking on Discord about a searchable VQC crumb database… you can CTRL F the Grid Patterns thread, bc the most relevant crumbs have been copypasta'd directly from VQC. Check it out. Thanks again AA for all your work, you grumpy faggot ;) Let's move the ball forward today, lads.
>>6506
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b5116b No.8260
Does anyone else here like math?
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df8366 No.8265
I think VQC recognised AA is about to unleash the solution.
That's why he became anonymous.
Alcoholism and fame do not go hand in hand.
Hopefully he can restart his recovery but I don't think he would want you to give up.
Perhaps as his recovery begins again, he will help anonymously.
It looks like the solution is focusing on how the patterns allow you to lookup two columns with n different by one for the d and d+1 cells you need for e,n and -f,n-1.
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df8366 No.8266
AA, the patterns you worked on are excellent. Outstanding.
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df8366 No.8267
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df8366 No.8268
>>8179
Never.
Anonymity is the Spiritual foundation.
You will Never give up.
Coincidence is God's will and method of staying anonymous.
You are close.
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8b4129 No.8269
>>8268
>>8265
You talk a lot like VQC for someone who isn't VQC.
>I think VQC recognised AA is about to unleash the solution.
If I am, I'm not consciously aware of it. As much as VQC (totally not you) did seem to think I would be the one to figure it out first in that one post, it would be pretty great if someone else did. I wouldn't want to get delusions of grandeur.
>>8266
>>8259
Thanks.
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8b4129 No.8270
If anyone didn't see, very important post in Grid Patterns by some anonymous stranger: >>8262
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df8366 No.8271
>>8269
I think it's important to ratchet up any help anons can give.
Your work in the patterns thread is excellent.
It's about figuring how to take that and create a lookup from the different types of input integers (c).
Once prime numbers are SIMPLE to spot, things should get a LOT easier.
There's already a polynomial time solution to identifying primes out there , if the grid can be used to speed that up, perhaps the penny might drop from that?
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abe23c No.8272
>>8252
>>8251
>>8254
It should be noted that when c = ab where a, b are two semi-primes then phi(c) = (a - 1)(b - 1) as phi(p) = p - 1 and phi(ab) = phi(a)phi(b).
I'm not sure it will hold for when a and b aren't semi primes.
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b129f9 No.8273
>>8272
Are you confusing prime and semiprime?
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8b4129 No.8275
>>8185
O(log n) means you divide the search area by two each time (e.g. binary search). So what does O(log n) where n is the length of c in bits mean? The only way it could translate is that your search area (for lack of a better term, not knowing the context) is c in base 2, and you’re dividing the search area (c in binary) by two each time you don’t successfully factorize. So what's the deal with this, anyway?
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8b4129 No.8276
>>7993
>lookup in gaps
>>7746
>It is a lookup via the x values in row 1.
But there are no gaps in row 1.
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83b459 No.8277
>>8276
What about Row 0?
Just for funsies.
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8b4129 No.8278
>>8277
There's nothing in row zero in positive (e) space, and in negative (f) space there are only cells in row zero where f is a square (so (-1,0), (-4,0), (-9,0) etc). It's not row one but it does have a relationship with row one in that all of the cells in (e,1) are also in (f,0). So I don't know if that was just an arbitrary thought or not but I guess that might actually be worth looking into.
All cells in (e,1) are in (f,0); (e,1) doesn't have gaps but (f,0) does (every f value that isn't square).
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cc56f4 No.8280
>>8278
>>8264
>The value at -f,n-1 and e,n have the same a,b but d,n, and x are different by 1.
>There is a way to use this to create the lookup.
Found something interesting studying the Grid:
For c145, the (e,1) d value is 12
The (-f) d value is 13
13^2 - 12^2 = 25 = (an)
Don't know if it works for other c values yet.
knowing that d is always one unit bigger in -f, you could make the hypothesis that (d+1)^2 - d^2 = (an)
I'll run some more c values to check if this in yet another c145 fluke.
Just studying the Grid and looking for patterns over here.
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8b4129 No.8282
>>8280
Definitely a 145 fluke. All odd numbers are the difference between two squares, but it's a series that scales linearly with the squares (well, linear with their square roots). https:// math.stackexchange.com/questions/136/why-are-the-differences-between-consecutive-squares-equal-to-the-sequence-of-odd
d and na don't scale linearly so it's not going to be the case for all of them (it also wasn't in the test cases I tried, for the record). 145 always seems to get everyone's hopes up.
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d45b18 No.8287
input = {d, e}
Since e has a column, what does d have?
We apologize for the inconvenience…
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8b4129 No.8288
>>8287
Based on your wording, it seems like you're implying a row. But all that boils down to is "use d to find n".
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5d6348 No.8289
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5d6348 No.8290
http:// empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/farey.htm
http:// archive.is/RUH4C
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abe23c No.8291
>>8273
Yes, it was late and my brain was mushy.
I got something I can't quite figure out. I suspect it's a fluke, but at the same time, it's a very convenient fluke. It's not limited to one cell, but multiple (e, n)'s. Not entirely sure how many.
I was playing with >>8260 and thinking about how our squares can be expressed as either 8 triangles + 1 or sum of two sets of 4 triangles depending on parity.
So assume k is even, then k + 1 is odd. That means we have 8T(u) + 1 - 4(Tu - T(u-1)). I was playing around with it, looking at what the numbers were for different cells and stuff, but then for some reason, (divine intervention?) I decided to just see what 8Tu - 4T(u + 1) was. Note here u is from d, so it's based only on the d within those rows.
I noticed in (3, 6) that 8T(u) - 4T(u + 1) (Again u is from d) was the smooth numbers for those cells. As in, if this pattern had held for ALL rows it would have been solved. It doesn't though, but it does for several others. Like (1, 5) and (11, 10).
Take any given cell from (1, 5) or (3, 6) or (11, 10) and probably a lot more and then calculate the u for d. Then calculate 8*T(u) - 4*T(u + 1). This will give you the smooth number for that cell. Then just take BigN - 8*T(u) - 4*T(u + 1) = n.
For other cells there appears to be an offset, as in the numbers are slightly off. I'm not sure why yet or even if this offset can be "known" based on certain other elements, but nevertheless it's the closest I've been to "touch" a solution.>>8260
Some offsets are limited to single integers for all the records in that row, while others move depending on different elements. Like I said, I haven't quite figured it out yet.
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2344ac No.8292
>>8170
I've written a script that computes remainder of any number when divided by (2^n)-1 only by summation and bit hacking.
It works by converting a number into series of digits in a chosen base and modulo summing the digits. As is, it works only for bases2^n, so for divisions of the form 2^n-1.
I think this can be further developed for any base, by treating each bit (when converting) not only as 0 or 1, but as a float between 0…1.
(pic related)
And with some clever bit hacking, we should be able to factorize any number stupidly quickly.
The code is written in C: https://pastebin.com/bj8U1Qb1
And can be tested online: https://www.onlinegdb.com/
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2344ac No.8293
>>8292
A crude algorithm for now.
But am thinking if we figure out how VQC came to his algorithm, we could figure out how the Grid works. As it was said a lot of times, the Grid is the solution.
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2344ac No.8294
Code that resembles a bit more what VQC posted: https://pastebin.com/5t67KA0f
This algorithm also generates a grid with base in column (array of n) and where each row contains digits (n[].d[]) that make up the original number (x) in observed base.
n[].r holds a value of x mod (base-1).
This algorithm still works only for (2^n)-1 divisions. Will try to extend to to any base. Any help,guidance or criticism is appreciated.
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b129f9 No.8295
>>8294
If you want people to help you, you'll need to give a lot more background on what led you to making this and the insights behind it.
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47d6d1 No.8298
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2344ac No.8299
>>8295
Yep sorry, will explain it more later. The uploaded code is wrong however, will work on it.
In the meantime, if we represent a value in some number base, base16: 0x3ab7, it means 7+b*16+a*16^2+3*16^3.
But the part b*16+a*16^2+3*16^3 is just sum of 16 (base) and 7 (remainder), the last digit is the remainder if 0x3ab7 divided by 16.
The problem I think we are solving is find a base b where last digit of a number is 0. Or rather construct a number in some base such that last digit is 0.
The base is then the solution. As number/base=0.
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2344ac No.8300
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8b4129 No.8301
>>8299
>The problem I think we are solving is find a base b where last digit of a number is 0.
And how did you come to that conclusion? Have you read through all of the threads?
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2344ac No.8302
Intuition :-) Also seems like a fun problem to work through.
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8b4129 No.8303
>>8302
I actually want to know, have you read through all of the threads?
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2344ac No.8304
No, not all. But the problem we are all solving is factorization. No?
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2344ac No.8305
>>8303
>VQC sez: "(You) are at The final lock and key construction steps. Happy to give it but it is the Eureka moment and anons are close. In hindsight, it shows exactly why this problem has existed for so long.You are solving two problems at once in this method of constructing the answer. Also in hindsight the steps give the pattern back in the grid (The End).
Maybe the answer is not in a decimal form but rather in some other base. Learning why and how the algorithm was constructed will reveal the answer.
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8b4129 No.8306
>>8304
>>8305
Okay, first of all, obviously you figured it out in that second post but you should really be quoting people you're responding to on this website. Secondly (and don't take this personally because it's an ongoing issue with this board that multiple people have contributed to now), do you actually understand specifically how we're working? Keep in mind, I have no malicious intent with this message, and for all I know you could be onto something useful, but people keep coming to this board, completely ignoring the specifics of the work we're doing, going through their own personal idea of what the point of this board is in relation to factorization, posting what they're working on, and wondering why nobody is responding to them or helping them with it. This has happened multiple times and you're doing the exact same thing. Another recent example is when that person who was messing with the Fibonacci sequence thought they'd solved it and all they'd done was iterate squares (which doesn't come close to solving the problem). You're welcome to keep working on your thing. Who knows, maybe you'll figure it out on your own. That is a genuine possibility. All I wanted to say is that there is a very slim chance of any of us working with you if you aren't actually going to get up to speed on the rest of our research. For example, do you know what (d+n)(d+n)-(x+n)(x+n) means? Do you know what d[t]-d=a(n-1) means? Because that's what the rest of us are working on.
Actually, one last thing.
>The problem I think we are solving is find a base b where last digit of a number is 0.
In base 2, everything that ends with a 0 is divisible by 2. In base 10, everything that ends with a 0 is divisible by 10. So if you take any number, the final digit will be 0 in any base for which the base is a factor. So if you take a prime number n, it'll only end with a 0 in base n. If you take a semiprime a*b=c, it'll only end in a 0 in bases a, b and c. So effectively you've rearranged the iteration method (the one we're trying to avoid because it's O(n)) into iterating bases. I would very strongly recommend reading all of the threads and getting a complete grip of the issue.
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2344ac No.8307
>>8306
The question still remains, why does it work the way it works.
You guys are too far in and too close, you work on yours and I will try something along a different path.
Who knows, maybe we can be of a help to one another.
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8b4129 No.8308
>>8307
Why does what work the way it works?
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83b459 No.8309
>>8307
I believe the term you're looking for is "tunnel visioned".
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ee3f1a No.8310
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ee3f1a No.8311
Watching this entire video will explain how discrete logarithms are calculated using the solution to integer factorization, and may even conta
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ee3f1a No.8312
We can state the problem of factorization as a discrete logarithm like so:
We pick any number that is relatively prime to c and call it k, (it is easy to find a relative prime, it is any number for which GCD(c, k) == 1).
Where ϕ(c) is Euler's totient function,
k^(ϕ(c)) ≡ 1 (mod c)
Read as: "k to the totient of c is congruent to 1 mod c." Thus, since it is easy to select a valid k, the factorization problem is restated as a discrete logarithm.
Using an example of 123, if we use 122 as k (GCD(123, 122) == 1), then 122^ϕ(123) ≡ 1 (mod c). We just have to calculate this exponent.
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ee3f1a No.8313
Are there any other equivalences of this problem?
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5d6348 No.8314
>>8305
base e is what you/they are looking for
it's base e
the natural base
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5d6348 No.8315
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5d6348 No.8316
http:// empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/p-adicsandadeles.htm
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abe23c No.8317
>>8314
So e is the natural base for numbers that exist within it's column?
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abe23c No.8318
>>8291
To follow up a bit on this one, I found a russian paper regarding pythagoras triples and fermats factorization. The paper outlines a method of iterating / finding all the pythagorian triples, which has a very nice correspondence to our grid.
Take the d from (0, e^2) and take the a from (e^2, 1) (Note the t-index in column e^2 has to be (e + 1)/2 to align the row with correct (0, e^2, t)) and then compute absolute(d^2 - a^2). It will give you a square.
I found this as I was looking to see if there was a pattern with regards to the differences as mentioned in the previous post (It appears to be a a part of the triplet, as in x, y or z from x^2 - y^2 = z^2).
It also appears that our smooth numbers exist in (0, e^2) as d-values, but I'm not entirely sure how to "get" the correct one yet. Given that with a large enough number the t-value for that smooth number would be too far down the list to find it iteratively. Although, we know that the smooth number has to be less than our N number, so it should cut down on the search space.
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b129f9 No.8319
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8b4129 No.8320
Hey Jan, in relation to >>8185 this, if you didn't already figure it out, taking the square root of a number halves its number of bits. So O(log t) where t is the length of c in bits refers to taking the square root of c over and over.
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3e929b No.8321
>>8319
>>8299
>>8305
Involves mandelbrot.
Mandelbrot set= f(c) = c^2 + c
and you do it over and over again.
1: c
2: c^2 + c
3: c^3 + c^2 + c
4: c^4 + c^3 + c^2+ c
5: c^5 + c^4 + c^3 + c^2 + c
The pattern is obviously going to continue like that.
If we are writing this in terms for c=2, for 4 we would get
2^5 + 2^4 + 2^3 + 2^2 + 2 = 30
30 in binary (base 2) is 11110.
multiply it by 273 which in binary is 100010001
This turns it into 1111111111110 (8190) which almost looks like a mersenne prime. but is just 12 bits long.
BUT with this you can turn multiplying these big numbers (30, 273) into smaller numbers,
This one is as easy as 4 * 3. If you look at pic related you can tell the it is just the length of four 1's (30) getting laid out next to a copy of itself 3 times and the result is 12 bits. Its kind of indicitive of how it can be used to multiply numbers where the length of the bits is 4.
If we multiliplied 1111 (15) by 273, we would get 111111111111 (4095) which is the same 4*3 but a different multiplication result. You could theoretically do this for 1111000…00 for any amount of zeros times 273 and you would get a length of 12 bits.
If you use a different c at the top, like 10, you would get
1: 10
2: 100 + 10
3: 1000 + 100 + 10
4: 10000 + 1000 + 100 + 10
So 4 is 11110 but in tens. Similarly we could do similar multiplication but it would be 1111111111110 but in decimal, so same look of the number, different meaning.
You could do this for any base. So if we could find the 'correct base' this could be the way to shrink the number to be a mersenne prime type number and then factor the length of that number. I'm not exactly sure how. Or we could convert the number to a length in bits of a certain base then factor that number.
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3e929b No.8322
>>8321
Then another thing we could look at with the changing bases is this, it looks like each number shares a number representation when you multiply it by 2.
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8b4129 No.8323
Okay what's the deal with this crumb?
>if a number at position t has a factor s at (e+1), then s is a factor at (s+1-t), (2s+1-t), etc for a at (e,1)
No matter how I interpret this in my testing, it doesn't work out. Before anyone says it, yes, my t calculation is right ((x+2)/2 for evens, (x+1)/2 for odds).
Here's an example.
(30,1,31) = {30:1:1875:60:1815:1937} f=-3721
This is the cell in (e,1) where t=(e+1). It's divisible by 11. So 11 should be a factor of a at (33+1-31)=3
(30,1,3) = {30:1:27:4:23:33} f=-25
23 is not divisible by 11.
But if interpreted differently (since it's a very poorly worded crumb in my opinion), maybe it refers to (e+1,1).
(31:1:5) = {31:1:65:9:56:76} f=-100
If a number at position t has a factor s at (e+1). (e+1) is 32.
(32:1:5) = {32:1:56:8:48:66} f=-81
48 is divisible by 12. So s should be a factor at (12+1-5)=8
(32:1:8) = {32:1:128:14:114:144} f=-225
114 is not divisible by 12.
What is this supposed to mean? I would really appreciate some help.
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b129f9 No.8324
>>8323
What's it from? Maybe I copied it by mistake
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8b4129 No.8325
>>8324
I took it from Grid Patterns, but I don't remember where it was when I originally put it into Grid Patterns. I remember it being VQC who said it but I might be wrong. He seemed to be the only one using s as a variable in this sense.
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abe23c No.8326
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abe23c No.8327
>>8326
He didn't specify all that much though. Are we sure he is referencing to the 'a' value in (e+1)?
In (e+1, 1) the d-values are the same as the a-values in (e, 1) in which case, if he was talking about (e+1, 1).d then it would be the same rule we've talked about before.
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8b4129 No.8328
>>8327
>>8324
It's basically the same wording as
>If an integer p is a factor of a[t], then p will be a factor of a[p+1-t] for ALL cells in row n=1
(which was VQC at the start of Grid Patterns), just without the (e+1). But I've found I have the same problem with this pattern as well. Whenever I try to apply it, the cell in question isn't a[p+1-t] away, it's a[p+2-t] away. The more I try to figure out why, the more I think I've done something wrong, but my t values are definitely as they should be. I have also seen several people in old threads and in Grid Patterns mention that they haven't been able to get this crumb to align with their grid. So have either of you tested with this one? I'm trying to sort Grid Patterns at the moment so it would be useful to figure out if I'm wrong or the crumb's wrong (I don't think I ever actually saw anyone use it, so I haven't seen confirmation, only confusion).
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b129f9 No.8329
>>8328
You should make the crumb right then. If it's off by one cell then change it to 2
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8b4129 No.8330
>>8329
I'm trying to verify if it's me or the crumb. That's why I'm asking someone else to check. VQC isn't often wrong.
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abe23c No.8331
>>8328
I had that issue a while ago too, and it was just how I computed the nth row that was wrong. Essentially I did my x-calculations wrong, leading me to always be off by one with regards to t.
Also yes, I tested that one.
If you make cN (c big N) and then compute c + 1 - t for that cell in (e, 1) you will get the cell in (e, 1) where a = cN' (Shadow n).
Example:
c = 259, n = 114
a[122] = 29526 (3, 1)
259 + 1 - 122 = 138
a[138] = 37814 (3, 1)
29526 / 259 = 114
37814 / 259 = 146 (shadow n)
Also note that 122 = 130 - 8 ((1 + 259)/2 = 130)
and 138 = 130 + 8 (also note 8 is half of d).
So cN and cN' exists in (e, 1) at t = (1+c)/2 - d/2 and t = (1+c)/2 + d/2.
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b129f9 No.8332
All products of odd numbers and all products of pairs of even numbers are the difference of two squares.
Different view of c%4==2
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b129f9 No.8333
"26 Holocaust's of a happening if VQC is legit. I am not joking."
I love me from the past.
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b129f9 No.8334
>>8332
odd*even = a multiple of 4 + 2
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8b4129 No.8335
Anyone ever figure out what this means?
>Each value of a in cell (1,1) is also the long side of an integer right angled triangle.
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8b4129 No.8336
>>8331
It does seem to work for c*BigN, yeah. But I can't get it to work for any of the other numbers I've tried. It always seems to be p+2-t for every number but c for some weird reason.
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c7aafd No.8337
c = -c
c = a*i + b*i
where i is the square root of minus one
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c7aafd No.8338
Someone asked where the totient value is?
Why don't you just switch e and f
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8b4129 No.8339
>>8335
Don't worry, I figured it out. https:// en.wikipedia.org/wiki/Kepler_triangle
The values of a in (1,1) are the only valid whole integers that work as hypotenuses based on a^2+b^2=c^2 (whatever that's called, something something Pythagoras, it's been a long time since I learned about that). So it boils down to a in (1,1) being the sum of two squares, which was already a well established pattern.
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Post last edited at
c7aafd No.8341
Did I mention that 2d+1 is just a rearranged polite number.
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8b4129 No.8342
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c7aafd No.8343
>>8338
Remember to divide by two if it doesn't exist
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8b4129 No.8344
This is not finished, but if anyone's brave enough to trust a pdf and has a spare minute or two to critique my formatting, it would be useful to know if I've structured the enumerated patterns well or if I should do anything differently. There are a couple of sections I'm going to add (like a list of the numbers that would solve the thing if we found them and such).
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d9a09d No.8345
Almost there AA. Your faith keeps me going.
Offset of 1 doesn't seem helpful at first does it. What about offset of 1 in a and b. Doesn't that give the factorization.
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8b4129 No.8346
>>8345
Already with the new IP huh? You don't waste time.
>Offset of 1 doesn't seem helpful at first does it. What about offset of 1 in a and b. Doesn't that give the factorization.
Yes it does. It gives 2(BigN-n). It also gives a cell for which (e+2n,n) is the solution record. The real question is how to get there with d and e, of course. If anyone reading this has time before me (I'm going to sleep soon), it would be useful to look at the cells in (e,1) and (f,1) where the x values add up to 2d+1 (maybe compare them to all the other (e,1)/(f,1) cells, since this is another calculatable).
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8b4129 No.8347
>>8345
>>8346
Well, if that's what you meant by an offset of 1, anyway.
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abe23c No.8348
>>8336
So 259 = 7x37
a[122] = 114 * 259 = 2*3*19 * 7*37
2 + 1 - 122 = -119
3 + 1 - 122 = -118
19 + 1 - 122 = -102
7 + 1 - 122 = -114
37 + 1 - 122 = -84
a[-119] = 28562
a[-118] = 28086
a[-102] = 21014
a[-114] = 26222
a[-84] = 14282
28562/2 = 14281
28086/3 = 9362
21014/19 = 1106
26222/7 = 3746
14282/37 = 386
It works, your code is not correct if you need a[p + 2 - t]. You're probably starting the index at zero instead of one. With the grid we start with the first cell in (e, 1) being index = 1.
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abe23c No.8349
At this point I wonder if the solution is staring us in the face, like we're glossing over the obvious pattern and we're not even realizing it.
Maybe it's the a[p + 1 - t], but in a way we haven't noticed or realized. Maybe the a[p + 1 - t] is a hint and not the solution. For example, do we have d[p + 1 - t] = something? Is it limited to a? what about x or some other variable like i, is the triangle also related in such a way? A whole cell? What if n is also somehow tied into that pattern. We know a is, so maybe there are similar patterns, but we got stuck on a[p + 1 - t]?
Just ranting a bit. And I want to say thank you again AA. You've been tremendous in gather the patterns, for real hands down MVP.
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5d6348 No.8350
>>8322
try natural logarithm base maybe, base e?
I don't know how that would work.
Or maybe base 60.
Sexagesimal.
Sumeria>Babylon>Egypt
It fits perfectly with how this whole mess started, and how we all ended up here conspiracy>Q>VQC.
Full circle.
It's perfect.
Also check out Babylonian fractions?
I think base 60 + Babylonian fractions would round this out nicely.
The more I think about this, the more I'm absolutely positive it's the key to you guys figuring this out.
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963d5d No.8351
>>8349
And I'm not going to lie, it sounds stupid saying "it's must be right in front of us" all the while this anonymous person is pretty much screaming "factorize d and e and look at farey trees and recursive functions". I personally haven't had time to look into them, but I'm guessing there is something there.
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8b4129 No.8352
>>8348
Maybe it would just be easier if I showed you my (e,1). There's nothing wrong with d or x, so I don't see why there would be anything wrong with t.
>>8349 (thanks)
>>8351
Pretty much all of the main points (other than specific hints like switching e and f for the totient value) that Not-VQC has been making for the past month or two have been "the fractal is based around d and e". It's been rephrased in very many ways, but that's the point. This only addresses the fractal. It doesn't address how you actually use the factors of d and e to factor c, which is the entire point of this board. So this is my thinking as to the logic behind it:
>you're meant to be able to factor c using d and e
>if you can't use d and e to directly factor c, you have to factor them, and so on, recursively (and since taking the square root of something halves the number of bits, this creates an algorithm that factors numbers in O(log n) time where n is the number of bits in c)
>there are three types of c for which a solution is already directly calculable (GCD(d,e)>1, e=0, f=(x+n)(x+n))
>if these don't work, we're meant to rely on factoring d and e to factor c (hence the decision tree wherein if you can't automatically factor c you bit trim and factor d and e - bit trimming turns numbers into the difference of two squares, meaning we can apply them to the grid and then multiply them by two to get them back to the original number)
>if we're meant to factor d and e to find c, and recursion stops once c is directly calculable, that means that in one particular layer of c, we're using both d, e and their factors/records/n values/incalculables (not just d and e, but also a layer down)
So something that would be useful to research would be finding all calculables and all incalculables for c but also for d, d's d, d's d's d and so on. It would also be useful to keep in mind the thing about bit trimming when doing this. We have a finite number of knowns and unknowns (although there are probably infinite knowns and unknowns, Not-VQC said a few days ago in Grid Patterns that the information required to factor c is definitely in that thread), and we have to bridge the gap between them. That doesn't mean a known is directly used to calculate an unknown. Otherwise we would be done already. It means that the solution lies in the application of everything: the big list of cells in (e,1) and (0,n), the concept that the a values in (e,1) are the sum of squares and the difference of squares (plus or minus a constant based on e), the various movements we can do horizontally from (0,n) (or from other origin points), the idea of triangle numbers and doubled squares turning up in (0,1), the idea of consecutive squares turning up in (1,1), the relationship between smooth numbers, (a-1)(b-1) and ab and (a-1)(b-1) having the same (x+n)(x+n), and the application of all of this to d and e recursively, comparing everything to the next value up in the tree. We wouldn't have learned about all of these things if it was going to be as simple as moving around throughout some records in (e,1). It also wouldn't be as hidden as it is if that were the case. Apologies for the wall of text.
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b129f9 No.8353
>>8344
I'm seeing a lot of discord in your formatting, I have some ideas for formatting it better but I'd have to know what you're using to make it.
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b129f9 No.8354
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18a709 No.8355
>>8352
I'm guessing you have some code that would generate the nth cell in a column?
I gave some examples above, but again in (3, 1) the cell at t=122 = {3:1:29769:243:29526:30014}
If you try to generate (3, 1, 122) what cell do you get? Also maybe you can post a the code-snippet you use to generate the nth function?
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b129f9 No.8356
>>8355
first coordinate = the column
second coordinate = the row
third coordinate = the index
first + second coordinate = the cell
first + second + third coordinate = the entry
record generation:
if (e is even): x = 2t - 2
if (e is odd): x = 2t - 1
a = (xx + e) / 2n
d = a + x
b = a + 2x + 2n
c = ab
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b129f9 No.8357
It is a 7 dimensional object indexed by coordinates of 3's. If you find things easy to picture in seven dimensions, why not try it.
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8b4129 No.8358
>>8355
It's the same as yours. I have a spreadsheet for (e,1) and (f,1) so I just use these >>8356 formulas for it.
I actually think this might be a problem of odd versus even. I've discovered that this works when e is odd but it's p+2-t for even e. Go to your (30,1).
(30:1:4) = {30:1:39:6:33:47} f=-49
33/11=3r0. 11+1-4=8.
(30:1:8) = {30:1:127:14:113:143} f=-225
113/11=10r3, so it doesn't work. However, at t+1,
(30:1:9) = {30:1:159:16:143:177} f=-289
143/11=13r0. p+2-t. Is yours like that?
But then using (3,1) (and I've now tested this on a couple other cells)
(3:1:4) = {3:1:33:7:26:42} f=-64
26/13=2r0. 13+1-4=10.
(3:1:10) = {3:1:201:19:182:222} f=-400
182/13=14r0. So it seems to work for odd e.
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abe23c No.8359
>>8358
Ah! Yes, sorry I kept thinking in odd e. Yeah for even e I think it's a[p + 2 - t]. PMA wrote about that a few threads ago.
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8b4129 No.8360
>>8359
I find it odd that VQC would neglect to mention that when he brought up that idea many times. Usually when he misses something out it's just the once.
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83b459 No.8361
>>8358
RIP TOOTS LIL' FIGHTER!!!
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b129f9 No.8363
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b129f9 No.8364
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f8a399 No.8365
Imagine conversion to base>1 as a case of division.
We have some value c and write it in some base, it is equivalent to dividing the number by base.
The result is a weighted sum of same digit (digit = base) + the remainder: think of c=a+ib, where a is remainder, i is sum of b(base).
And knowing only (a,i) is enough for us to reconstruct c. a,i are unique result for any b. Meaning there is only one way that c could be written by division.
Can we extend this to multiplication? Maybe 0<base<1.
When we multiply(change base<1) a number the result is no longer unique as there would be multiple way for us to reach the same number by a different multiplication (base).
In multiplication the result is not a weighted sum of the same digit (not equally split) but rather a combination of all digits. In case of multiplying by 10 (base1/10) I'd imagine it would be a weighted sum of 0,1,1/2,1/3,1/4,…1/9.
The result in this case is not unique and cannot be written by just two variables.
Can multiplication be represented as fractional base? If it could be lets define negative base as 1/base: b=-10 would be base10^-1.
Lets make a spreadsheet.
c on x axis (c-c..c-2,c-1,c+0,c+1,c+2..c+c) and base b on y axis (c…2,1,0,1,2…c).
And each cell containing r=remainder (first digit) or some other data.
The goal is to find a way around this grid from the origin (base=b, c=c+0) to a cell where r=0 (base=factor of c). Can we use fractals to help?
Just some thoughts. Will try to make more sense of fractional bases later and write a script. Maybe its an equivalent problem to what VQC is proposing.
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83b459 No.8366
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cbe267 No.8367
Has anyone looked at a number with quite a few factors, calculated it's values for e and f, then looked at the different values for n at column e, and n-1 at column -f?
There will be multiple pairs of n and n-1.
Wouldn't any lookup be easier to see and model at first in integers with lots of factors?
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83b5cf No.8368
Alright, found something interesting. Since this is supposed to be a lookup for the correct x value in (e,1) or (-f,1) I assumed that the correct x value must be related to the na transform record in a fractal / golden mean ratio.
I took the (e na transform) and (-f na transform) records for c145 and c287.
For c145 (e na) the x value is 11.
11 / 1.61 (golden ratio) = 6.823 = very close to x=7, which is the correct x for the (an) and (prime) elements.
For c287 (e na) the x value is 15.
15 / 1.61 (golden ratio) = 9.31677 = very close to 9, which is the correct x for the (an) and (prime) elements.
I have only tested these two c values, so any additional help you Anons can provide to test other c values would be greatly appreciated.
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83b5cf No.8369
>>8368
Also, the (bn) records can be almost obtained in the same way.
for c287, (e na) x = 15. 15 * 1.61 = 24.15 = very close to correct (bn) x = 25
for c145, (e na) x = 11. 11 * 1.61 = 17.71 = very close to correct (bn) x = 17
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b129f9 No.8370
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8b4129 No.8371
Hey Not-VQC, I'm curious about something. I'm not asking for a hint right now, but I think the perspective of someone who figured it out already would be useful. If you were in our position, and you had this giant set of information but absolutely no idea what to do with any of it, what would you do? When you enumerated all of the patterns, what was your next step?
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891f44 No.8372
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891f44 No.8373
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891f44 No.8374
Directed -> Nondirected thinking.
Algorithm -> Art.
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fd645c No.8375
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b129f9 No.8376
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83b459 No.8377
https://danielmiessler.com/study/pvsnp/
"So the P vs NP problem is just asking if these two problem types are the same, or if they are different, i.e. that there are some problems that are easily verified but not easily solved."
Soooo… by completing and running the VQC… we literally prove P=NP?
What is/was/should be a "not easily solvable problem" becomes "easily solvable and verified".
Or like…
"For the longest time we thought it was hard as fuck and not possible to do this, but it turns out it is possible and had been known about for quite some time. Fuckers."
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8b4129 No.8378
The a values in (-1,4) are the sequence of triangle numbers. The a values in (-1,2) are two times the sequence of triangle numbers.
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8b4129 No.8379
Every d value in (-1,1) is two times a square minus 1 (this is also the sequence of ns in (0,n) where a and b are both squares but with each value minus 1).
Every a and b value in (-1,1) is four times the triangle numbers. They add together to make every even square (so every even (x+n)(x+n) is in here (4T(u)+4T(u-1)), as well as 2(x+n)(x+n) for odd (x+n)(x+n)). So since a+b only comes up in the n equation n=((a+b)/2)-d, you could rearrange it such that the a+b you want, which comes from (x+n)(x+n), equals 2(d+n) for (-1,1). For example, 4+12=2(7+1). Since d here is two times a square minus 1, but a+b=2(d+1), and if you add 1 to d you’ll have a square multiplied by 2, you’ll by multiplying twice a square by 2, making it 4*square. All a+b values in (-1,1) are equal to 4 times a square, and all a+b values in (-1,1) represent every possible even square.
4+12=16, 16/4=4 (2*2)
12+24=36, 36/4=9 (3*3)
24+40=64, 64/4=16 (4*4)
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8b4129 No.8380
>>8373
>metacognition
>Metacognition is "cognition about cognition", "thinking about thinking", "knowing about knowing", becoming "aware of one's awareness" and higher-order thinking skills
I tried to start a discussion about where recursion actually comes in on Discord a little while ago but everyone ignored me. Maybe if I bring it up here it'll gain traction. We need to take a step back and put all of the patterns and such into context within the algorithm. What we have is a big list of patterns and cells. What we need is a recursive algorithm.
How is it that we can actually use the grid recursively around d and e? The idea that we need to bit-trim d and e in order to factor c means that we don't have enough information about c just from d and e in order to find the correct record/the lookup x/the na record/the triangle base/etc. We have a giant list of rules, movements and patterns that are meant to be used. However, the fact that we need to factor d and e through the factor tree unless c is immediately factorable (through GCD, e=0 or f=(x+n)(x+n)) means that there isn't enough information just from that big list of patterns. We've been taking an incorrect approach to this for quite some time, I think. Everything I see any of us looking into (including myself of course) is related to finding connections between the finite set of cells that we're aware we can generate with our prime solution record. If there was any possibility that we could bridge a gap between the BigN cell and the prime solution record entirely with patterns revolving around c, not only would it completely bypass the bit-trim factor tree, but it wouldn't be recursive at all. It would be O(1). Where c is immediately factorized is the recursion termination point. We factor d and e recursively (that's what VQC said a bunch of times).
So what is the missing link between a factorization of d and e and a factorization of c? Looking into anything else isn't going to solve it; it's just going to expand our list of patterns. This idea of metacognition is actually extremely useful right now (thanks Chris).
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125cd1 No.8381
>>8380
Just to nitpick it would be O(sqrt) as we do compute the sqrt of c to get d. That is the upper limit in the case you're describing.
I see the bit trimming as a means to simplify. When we trim bits we simply remove 2 as a factor, leaving us with factors beyond 2. I'm not sure why, but the number 2 appears to be "special" in the grid. Several times I've seen patterns where I expect the result to contain 2x2x…, but instead contain 2x… (One less factor of 2 than I expected).
I've said it before, but I suspect that VQC has been giving us hints related to all the keys he knows. The recursive one I suspect is one method. The triangle one is another and I suspect the (n-1)naa is a third.
How factorizing d and e solves it, I'm not sure. We know that if gcd(d, e) != 1, then we have the d = kq (for some k and q) and e = ko (for some k, o) which gives us: kqkq + ko => k(qq + o). I wonder if, when solving d and e we will end up with something similar that we can then use to "figure it out". It's the figure it out part that's hard and recusing over d and e doesn't give me any good ideas about how to solve it.
As for the subject, metacognition, I'm wonder what do we have? We have a huge grid, that exists as a lookup and we know that column 0 (row 1?) is supposed to operate as the QFT (Quantum Fourier Transformation), but just writing this doesn't make me understand it.
The grid shows us how numbers can be grouped together as the difference of two squares, and how this two squares are related to the integer and the integers factors.
We have patterns inside the grid for knowing how a cell is related to other cells in different columns. We can move in many ways, by shrinking or increasing the largest square we remove from the number. By transforming the number, but so far we haven't actually gotten a solution.
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125cd1 No.8382
>>8380
I'm ranting a bit I know, but I'm trying to think loud.
If we assume the recursive method is the solution, then I'm wondering more about the patterns we spend time on. Are they then irrelevant? Or are they irrelevant for the problem at hand, but useful once you understand the grid? As in, will the grid be used further to solve other problems?
Based on the description of the recursive method, we only need to care about d and e. We generate a tree where we branch out from d and e, but for each node we only store d and e (and c?). However, we know that doing so doesn't solve for all d and e. As in, gcd(d, e) doesn't solve much, we still have branches that aren't solved, and I think I've seen "trees" where none of the nodes are solved using just that method. Which means, we're missing something.
Assume we're building a tree, where each node contains three values, d, e and c. c is the input number of the node, d and e are the d and e-values of the c-value. This tree is what the recursive algorithm gives us, but we aren't done yet.
What then would be the next logical step? How would you connect this tree to the grid? We have an initial c, we have a tree. We can move recursively down the tree and then what?
To digress a bit, I remember in one of the first threads, VQC talked about multiplying our c number with other numbers. As a means to create a column that is predictable and that we "control". From this column we could coax out the factors of c, did we ever to much with this? Was it just something to get us interested? Knowing now what we know, is that a possibility?
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566843 No.8383
>>8350
If we look at any number base, the 1's place is 1, the next place is b, the next is b*b, then b*b*b etc. Obviously, you can't really have non-integers as bases and e=2.718 is a decimal.
In a way, though, the fibonacci numbers are like base e. because F(n) * phi ~= F(n+1), which is similar to how, in base 10 for example, if you have 7 * 10 = 70.
Sexagesimal again obvious pointer to fibonacci numbers. (great site btw)
https://www.mathsisfun.com/numbers/fibonacci-sequence.html
If you look at the last digit of fibonacci numbers it repeats every 60. The tens repeats every 300, etc.
>Full circle
Implication we need to use a circle.
>It's perfect
Perfect circle
>I think base 60 + Babylonian fractions would round this out nicely
>round this out
Either another reference to the roundness of a circle or has to do with rounding the numbers.
>Absolutely positive its the key
Absolute value of something
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577a00 No.8384
>>8377
Factoring isn't known to be NP-hard, so solving it wouldn't necessarily prove P=NP.
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566843 No.8385
I gotta go back to work, but I thikn we could do something with this notation
If we have an number like:
'100001000' in fibonacci notation,
we could rewrite it as
'100000110'
or
'011000110'
'002100110'
'000320110'
'000053110'
etc.
Like any number can be turned into the two next to it.
I think that if we can make this a constant digit then it must be divisible by that digit at the very least.
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83b459 No.8386
>>8378
in bold: 1+2+3+4+5+6+7… etc.
>>8381
I've tried explaining the Limits I see, c/2 and √c, with my Masonic Square'n'Compass but it only gets remembered every now and then.
>>8384
Factoring a Google length RSA Semi-Prime into its Co-Primes isn't "NP-hard"? Well that's gay.
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fd645c No.8387
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8b4129 No.8388
>>8381
>it would be O(sqrt)
O(sqrt) is O(log n) where n is the length of c in bits, which is what VQC has always said. Taking the square root of something halves its number of bits.
>I see the bit trimming as a means to simplify.
>I suspect that VQC has been giving us hints related to all the keys he knows. The recursive one I suspect is one method. The triangle one is another and I suspect the (n-1)naa is a third.
If the recursive solution was one of several methods, there would be one O(log n) method and several O(1) methods. The only way anything VQC has said makes any sense is if every method relies on factoring d and e. That means we have to know the factors of d and e to solve. That means there isn't enough information purely from c to solve.
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abe23c No.8389
>>8388
No it wouldn't be O(1). So far, everything involved requires us to calculate d which would require O(sqrt) (or O(log n) as you put it).
If we need to go recursive and we need to factor d and e, does that mean the other approaches VQC has talked about in the past (triangle, -f and e … ) are just approaches that won't work (or will, but with a too high complexity)? Or do you think it all ties in together?
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8b4129 No.8390
>>8389
If we only calculate d and e for one c, it isn't O(log n). It's O(log n) if we calculate d and e continually, because in the worst case we would halve the number of bits log n times (but we wouldn't always have to do that). If we were only meant to calculate d and e for one c, it would be O(sqrt), which is different, and definitely not what VQC said.
>If we need to go recursive and we need to factor d and e, does that mean the other approaches VQC has talked about in the past (triangle, -f and e … ) are just approaches that won't work (or will, but with a too high complexity)? Or do you think it all ties in together?
My theory is that we use those approaches in conjunction with factored d and e. We wouldn't have learned those things for no reason. My theory is that we use a fully factored d and e in order to apply those approaches that we currently can't use. So the cells and numbers for 5*29=145 could be used to factor other numbers for which d=145, maybe.
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b129f9 No.8391
Good insights, AA. Since factorizing d and e enable the factorization of c, then that also means that the patterns in the factorization of d apply to every number inbetween d^2 and (d+1)^2.
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b129f9 No.8393
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b129f9 No.8394
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b129f9 No.8395
notice how only one n is taken up between each square?
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5d6348 No.8396
Recombination = DNA
2 equations that spiral around each other
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609e7d No.8397
>>8396
AA and Jan, since we're not that many people left still discussing things I'm asking you two a bit more directly. Have we identified any of these two equations VQC has talked about? I know we have a lot of equations and he has talked in the past about two branches of math meeting, solving two equations in tandem(?)/parallel only to have them meet and combine, which will become a new thing.
My initial though is that he might be referring to the multiplication of -f and e. Since we know they will not be of the same parity, we then also know that they will have a different set of equations for the a-values. If f is even then a's are 2 squares - f/2, and a-values in e will be 4 triangles + (e + 1)/2. If f is odd then a's are 4 triangles - (f - 1)/2 and e will be 2 squares + e/2. These are two "different" equations, meeting (in the exclusive middle?).
But how would those spiral?
Also to note, I'm asking because I'm not sure, but I personally doubt that we're talking about the equations for 'a' alone here.
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609e7d No.8398
>>8397
Based on previous posts and work we've done, I would assume that one of the equations is nn + 2d(n - 1) + f - 1. Or PMA's suggestion of nn + (2d - 1)(n - 1) + n - 1 + f - 1.
Assuming that is true, and we're going to combine the triangular solution with the recursive function, then we will end up with a tree and parts of that equation. We'll know 2d, f and -2. Somehow, this is going to be connected to the tree and the grid.
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8b4129 No.8399
>>8397
>two equations
>spiral
Wut
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566843 No.8400
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566843 No.8401
Heres some examples for shrinking the fibonacci notation down. First is for full notations.
Next is if you keep it as 1's and 0's. I think that is the better route to take but idk why I say that. It seems that the most sparse it will be is always 101010101 etc and the most dense is 11111111. Basically the rule of this when you collapse it is that it is 1s broken up by 0s and there are never two zeroes touching, because if there were then you could populate them with the next higher digit. If you have a streak of 1's (aka a sum of consecutive fibonacci numbers) then it is as follows
>https://math.stackexchange.com/questions/833231/the-sum-of-n-consecutive-fibonacci-numbers
Sum of (F(1) .. F(k)) = F(k+2) - 1
So the sum from j to k would be:
[F(k+2) - 1] - [F(j+2) - 1] = F(k+2) - F(j+2)
I don't know where you'd fit in the negatives. Maybe make a second number. Basically I'm thinking we collapse it until we can't anymore then trim out the streaks by removing the negative element, then keep collapsing until its just a string of 1's then do something with the negative
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566843 No.8402
>>8401
This could also be like 12 steps
>take deep inventory of self
>take out the bad (negatives)
>do something with it at the end (give to friend or something)
>maybe thats the original number
>idk im sleepy
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b129f9 No.8403
Anyone have a copy of the old threads that includes pictures? The archive only saved the thumbnails
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b129f9 No.8404
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566843 No.8405
>Admitting powerlessness over the addiction and our lives had become unmanageable
Powerless AKA not a difference of squares. AKA 1 dimensional.
If our lives were manageable then we'd have two factors for it
>Believing that a higher power (in whatever form) can help
I think this higher power is phi and in specific this big spiral.
>Deciding to turn control over to the higher power
I think this would be to represent ones self as a sum of fibonacci numbers (none consecutive)
For example 3*5 = 15 would be 13 + 2 = 1000100 = (13)(0)(0)(0)(2)(0)(0)
>Taking a personal inventory
[Interesting how 145 = 144 + 1 and 144 and 1 are both fibonacci numbers]
I think this is to look at your own bits within the number.
(this is just my idea for now of what this entails)
1000100
0110011
0101111
This streak of four 1's is 1+1+2+3 = 7
The 1 on the left is 8
7+8 = 15
>>8401
Sum of consecutive fibs = F(1) + … + F(k) = F(k+2) - 1
15 = 0101111 = 0100000 + 0001111
and 0001111 = 0100000 - 1
15 = 0100000 + 0100000 - 1
15 = 0111000 - 1
15 = 0110110 - 1
15 = 0110110 - 1 = 0110000 + 0000110 - 0000001
0000110 = 0010000 - 0001000
0110000 = 10000000 - 1000000
so
15 = 10000000 + 0010000 - [ 0001000 + 1000000 - 0000001 ]
15 = 10010000 - 1001001
15 = 10001100 - 0110111
15 = 10001011 - 0110111
etc..
>Admitting to the higher power, oneself, and another person the wrongs done
Something something get the negative amount and give it to the fibonacci
15 = 1000100 = 1111111 - 0111011 Maybe this value is the negative.
>Being ready to have the higher power correct any shortcomings in one’s character
Correction of shorcomings would be the result of this calculation whatever that may be
>Asking the higher power to remove those shortcomings
Subtract that amount from you
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708ece No.8406
Have we considered using "Imaginary Phi"?
https:// math.stackexchange.com/questions/1851698/imaginary-golden-ratio
>Some joke about radicalization and flying complex planes into buildings
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708ece No.8407
http:// mymathforum.com/number-theory/17605-imaginary-golden-ratio.html
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cbe267 No.8408
Is it possible that if we multiply c by a certain number, say q, and get the remainder e, given that we can calculate -f, we can force the resulting -f and e columns to create our lookup?
Thinking outside the box, what if actually multiplying c by certain value or values, forces the result to be where we want, to make the lookup easier.
We could theorectically do it in two steps, getting information from the first product, qc, and introduce a second factor, v, again forcing the result to give us a deterministic result for e and -f. This product, vqc, could then be used to "triangulate" a lookup somehow?
The chosen numbers for v and q may depend on the type of c we are using but I would speculate they would be from a limited set…
This approach would still be O(log l) or less, where log l is the length of c in bits because the largest operation remains finding a square root and remainder. It doesn't matter if we need to do it more than once, the overall complexity in Big Oh remains the same.
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b129f9 No.8411
On the occasion of the death of 41:
"When his breath departs, he returns to the Earth. On that day his plans perish."
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83b459 No.8412
YouTube embed. Click thumbnail to play. If I posted this already, it woulda been months ago.
If you haven't seen it already, give it a look-see.
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83b459 No.8413
YouTube embed. Click thumbnail to play. Judging the video by the thumbnail (book by the cover)… looks familiar…
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566843 No.8414
Anybody want some grids? More incoming
In order that is E by A
E by C
E by D
E by (d+n)
E by F
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566843 No.8415
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566843 No.8416
>>8415
E by D+N
X by E with F highlighted
Edge of where I could generate the X by X+N grid
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8b4129 No.8417
Crap, missed our anniversary by a day
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b129f9 No.8418
>>8417
Happy anniversary! Cheers to that walkthrough by Christmas!
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83b459 No.8419
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01587d No.8420
For c6107, interesting that our u1 and u2 values are 41 and 42, since our f derived polite numbers = 3+4=7
The total x+n dimensions are 83 * 83 = 6889.
4 rectangles of 41 * 42 +1 = 6889
It’s the (n-1) pattern playing out at 2 levels simultaneously.
Maybe a fluke, just brainstorming over here.
c6107 f= 134
f div 8 = 16
Sqrt(16) = 4
Sqrt(16)- 1 = 3
4+3=7. These are our two polite triangle number bases added together.
7 * unknown + 1 = correct (x+n)^2
For this example it turns out to be 984.
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01587d No.8421
>>8420
This should be blazing fast at computer calc speed! since the two polite triangle bases come from f, it should scale upwards with increasing c values.
All we have to do is check each iteration to see if it's a perfect square.
This is the two equations merging together or running alongside each other. (i think)
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5d6348 No.8422
http:// archive.is/q3szP
looks familiar
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174e7d No.8423
>>8422
Farey Tree Anon, I studied that Plimpton 322 article. Hilarious that all this probably started as a project cost analysis for some engineer or business manager ~6000 years ago. Like "Shit guys we gotta figure out the dimensions of this ramp some we know how much limestone to order from the quarry for this 1000 cubit length ramp. Go figure this shit out, we're on the King's payroll anyways, and we don't want too many slaves dying hauling extra rock from the quarry if we're gonna make our deadlines. Tell that fucking nerdy kid who sits around thinking all day to figure it out. He's a fucking weirdo, oh well, he's great at drawing triangles all day."
Thus was born the First Autist, lol.
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5d6348 No.8424
>>8423
Lol. It is funny isn't it, how everything seems to connect. Maybe history can provide the perspective needed to finish this thing.
I found this short read to be extremely good.
https:// www.google.com/url?sa=t&source=web&rct=j&url=http://vixra.org/pdf/1407.0062v1.pdf&ved=2ahUKEwjkpbXY84HfAhWMwMQHHVioDawQFjAQegQIBRAB&usg=AOvVaw1mZHbw_xNX0CbQ4bx-tmQA
Why Base 60 by JF Sweeney if you want to google the link yourself
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174e7d No.8425
>>8424
>>8420
Here’s another example, this time for even x+n
Even (x+n)^2 = 144
f=2d+1-e = 24
Sqrt(24) = 4 r 8
4 * 36 =144
The factor will scale with c, since it's derived from f.
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174e7d No.8426
>>8425
This was why VQC told us we would be estimating n0 when we used the (f-1) div 8 method. We’re looking for a way to use f to construct (x+n)^2
Correction: this is one of the ways to do it. There are multiple correct methods.
I’m just working on the one that I understand the most.
Can we try it out on the RSA100 Numbers we have all the solutions for?
Essentially I'm postulating that (x+n)^2 is a multiple of f or one of its roots, so a big difference from just (x+n).
The factor derived from f * iteration forms / fills the area of the square.
Odd (x+n) formula is f * unknown + 1 = (x+n)^2
Even (x+n) formula is f * unknown = (x+n)^2 (possible)
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83b459 No.8427
Does VQC stand for "The Vector of Every C"?
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366f62 No.8429
>>8426
Since the two polite triangle bases come from f, it should scale upwards with increasing c values.
All we have to do is check each iteration to see if it's a perfect square.
This is the two equations merging together or running alongside each other. (i think)
Equation 1 is: SQRT(c + (x+n)^2) - d = n
Equation 2 is: f factor * iteration + 1 = a perfect square? If not, don't run it through equation 1.
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366f62 No.8430
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a4498f No.8431
Enumerating e in a given row n is a way of enumerating every possible n value in an intelligent way.
If we swap n and x coordinate wise, we can enumerate x values the same way we did n values. The horizontal gap in every other cell highlights the fact that only every other x value is defined in a cell. (Hence, cells have either odd or even x values).
What type of movement would this be?
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8b4129 No.8432
I wrote a program (in Java) that creates the factor tree and generates every relevant cell and value that we've studied throughout the tree for each c/d/e/d's d/d's e/etc. You need the GridCell class I wrote for it to work (also below). I didn't bit-trim throughout the tree. I just divided each number by two until it was the difference of two squares (so it has evens that are divisible by 4 and odds). It also isn't done with BigInteger. I'll have to rewrite both programs with BigInteger at some point because it isn't completely functional without BigInteger (for example, generating the cells in (e,1) and (f,1) where c*BigN and c*(BigN-1) creates integer overflows). Either way, here it is. My thought is that it'll be quite useful to look for patterns that occur between all relevant information for c and all relevant information for d and e.
everything.java - https://pastebin.com/mbH8eZ7s
GridCell.java - https://pastebin.com/Cn36RwPA
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a3777e No.8433
>>8432
Got a present for you AA anon.
Where a value, c first appear in row 1 at e for the value a[1], t=1?That is a column e.
Where does it next appear in row 1 at a different e for the value a[t], t=2?
And so on back towards the origin.
Every column that c appears in has what in common?
How many columns do you need to create a lookup?
What specific information does that set of columns build up?
We know a and b are values of n in EVERY one of these columns because c is in the first cell of each column for a value of a[t].
Once you 'c' it, you cannot unsee it.
Godspeed anon.
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a3777e No.8434
Use RSA100 as a known large integer, if you can.
If your method works for that, you'll be just about set.
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8b4129 No.8435
>>8433
>>8434
I can't tell if the whole "AA anon" thing is a joke, but, if you didn't realize, the second A stands for anon. I'll have to look into this tonight. Any reason why it's specifically addressed to me?
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a3777e No.8436
>>8435
This was never about me.
It's about You.
It's about us.
The larger a number c, the more columns it is in, the more information about c is in the number c, the easier the lookup.
The single most important takeaway is that you now have a method that gives you more information about c the larger it is, not less.
Important.
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a3777e No.8437
One of the most important prayers that exist is when two or more gather in His name, that they spare a moment for all still suffering anon both inside and outside the rooms regardless of time sober.
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8b4129 No.8438
>>8433
>Got a present for you AA anon.
>Where a value, c first appear in row 1 at e for the value a[1], t=1?That is a column e.
If c is semiprime and the difference of two squares, it'll be odd. Any odd number c appears as a[1] at (2c,1), since for even e in (e,1) a[t]=e/2+2(t-1)(t-1), and a[1] is e/2+2(1-1)(1-1)=e/2. So for example c145 appears as e[1] at (290:1:1) = {290:1:145:0:145:147} f=-1. It'll also appear as a[1] at (2c-1,1), since for odd e in (e,1) a[t]=(e-1)/2+(t-1)(t-1)+tt, and a[1] is (e-1)/2+(1-1)(1-1)+(1*1)=(e-1)/2+1. (289:1:1) = {289:1:146:1:145:149} f=-4
To simplify: since all a values in (e,1) are twice a square or the sum of consecutive squares (based around t) plus either e/2 or (e-1)/2, but we're choosing t, we can just take 2(t-1)(t-1) and (t-1)(t-1)+tt away from c to find e/2 or (e-1)/2 and therefore calculate the columns in which c will appear as an a value in (e,1).
>Where does it next appear in row 1 at a different e for the value a[t], t=2?
2(2-1)(2-1)=2, and 145-2=143, and then 143*2=286, so it'll appear in (286:1:2) = {286:1:147:2:145:151} f=-9. (2-1)(2-1)+(2*2)=5, 145-5=140, and (140*2)+1=281, so it'll appear in (281:1:2) = {281:1:148:3:145:153} f=-16
>And so on back towards the origin.
Where c145 appears as a[t] in (e,1) with t increasing from 1 upwards, to begin with for even e is 290, 286, 274, 254, 226, 190, etc. -4, -12, -20, -28 etc. The gap between cells increases by 8 each time for even e. For odd e, 289, 281, 265, 241, 209, 169, etc. -8, -16, -24, -32, etc. The gap between cells also increases by 8 each time, but the first started at 4 and this one starts at 8.
>Every column that c appears in has what in common?
They're all in (e,1) so they follow the (e,1) patterns of every factor of this particular number having a valid n in this column. So in every column that follows the above pattern, there'll be a valid cell at the a and b we're trying to find. There are probably other things but I'm assuming that's your point.
>How many columns do you need to create a lookup?
That depends on what other information is required for the lookup, and we don't know that.
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2bc45b No.8440
(-238, 1, 12) = {-238:1:145:22:123:169}
(-286, 1, 13) = {-286:1:169:24:145:195}
(574, 1, 2) = {574:1:291:2:289:295}
(-1798, 1, 31) = {-1798:1:961:60:901:1023}
(-5742, 1, 68) = {-5742:1:6241:134:6107:6377}
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2bc45b No.8441
>>8438
That makes me wonder if that's why we were taking things over eight
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8b4129 No.8442
I've rewritten my program that outputs everything from Grid Patterns (unless I missed something) down the recursive d/e factor tree for BigInteger. Pic related is a small section of example output. You need the following two java files:
https://pastebin.com/mvrvxVr4
https://pastebin.com/NjGYV8ip
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bf321c No.8443
Hello Anons! I noticed that the Polite Triangle Bases for c6107 = 7 and (n-1) = 35 = 7 * 5.
Is this just a fluke?
For c145, PTB = 1+0=1 and (n-1) = 4 = 1 * 4
"A few more iterations and you have the Grid related short cut!!!"
Let's run a few other c values a bit larger and see if the PTB's are factors of (n-1)
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83b459 No.8448
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b129f9 No.8449
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abe23c No.8450
>>8449
Almost, you're missing half of them. So we can reason a simple method of finding the e's without the need for brute forcing by just using algebra.
We have two equations, one for even e and one for odd e.
even e:
2(t - 1)(t - 1) + e/2 = a
odd e:
2t(t-1) + (e+1)/2 = a
What we're talking about now is solving for a, which will be our c.
2(t - 1)(t - 1) + e/2 = a
4(t - 1)(t - 1) + e = 2a
e = 2a - 4(t - 1)(t - 1)
2t(t-1) + (e + 1)/2 = a
4t(t-1) + e + 1 = a
e = 2a - 4t(t-1) - 1
Example:
We want to find which e's a[1] = 145. There's two of them.
290 = 2*145 - 4*0*0
289 = 2*145 - 4*1*0 - 1
Since a[1] is a bit bland, let's find the e where a[3105] = 145
2*145 - 4*3104*3104 = -38538974
2*145 - 4*3105*3104 - 1 = -38551391
And the records in the cells:
{-38538974:1:6353:6208:145:12563}
{-38551391:1:6354:6209:145:12565}
You can also use this to find columns where c exists in a specific n (for some e).
Say we want to find the columns where there is an a[t] = 145 in (e, 5).
2*5*145 - 4*t*(t-1) - 1
2*5*145 - 4*(t-1)*(t-1)
This takes advantage of the fact that if 5*145 exists in (e, 1) then 145 exists as an a in (e, 5) (At the same time 5 exists in (e, 145)).
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b47fbb No.8451
>>8450
Did you try it on an RSA number ?
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b129f9 No.8452
>>8451
Making progress. Didn't factor any RSA numbers but I factored their d values each in one iteration
https://pastebin.com/9rBsXZU6
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abe23c No.8453
>>8451
Yeah. It's kind of hard to verify that it generates the accurate records. I'm not 100% sure since the numbers are so big, but it appears to work for smaller numbers, so I think it's fine. I included the first records for RS100: https://pastebin.com/nart63j2
One thing I noticed while checking with regards to smaller numbers (so it could be a fluke) is that all the e's where c exists in row 1 are also numbers that are part of phi(2c) with a few exceptions (ie a few numbers that divide c). I was looking into it to see if that meant we could take advantage of this to factorize, but that is still no dice given the amount of values to iterate over for a large number.
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abe23c No.8454
I was thinking about >>8433 and why we're looking at c at a[1], a[2].. and I started to think about these hints from a while ago:
> When does c first appear at a[t]?
> When is the second time it appears?
I decided to see how many E's squared numbers appear in. The number of e's per square correlate with the Beatty sequence (A001951). That is, 1*1 appears in column 1, 2*2 appears in 2 columns, 3*3 appears in 4 columns… The number of e's that the first 72 squares have match the numerical sequence of Beatty sequence for floor(n*sqrt(2)).
I did a quick check against the first 5000 squares and the first 5000 values of floor(n*sqrt(2)) and it appears to check out.
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23fc27 No.8456
72 + 73
27+28+29+30+31
10+11+12+13+14+15+16+17+18+19
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83b459 No.8457
>>8456
>72 + 73=145
>27+28+29+30+31=145
>10+11+12+13+14+15+16+17+18+19=145
77+78=155
29+30+31+32+33=155
11+12+13+14+15+16+17+18+19+20=155
(jump 5) 82+83=165
(jump 2… yup) 31+32+33+34+35=165
12+13+14+15+16+17+18+19+20+21=165
—–
Let's start with 145 as our base
You build from the bottom, so you start with your lowest value set.
GCD or HCF is the middle number in the middle value set.
Top value set is your sum/2, and then you make 'em whole numbers by adding remaining .5 to one of 'em.
145 -> 155 -> 165 (avg + 5, sum +10)
29 -> 31 -> 33 (HCF +2)
10 -> 11 -> 12 (base +1, 10 numbers {thus sum increases by 10 each time})
So your sum that you're working with will shift by n, where n=number of values being summed (in your lower value set)
I don't know if this holds, but the middle value set has half the amount of numbers as the lower set, so n/2=n'
Which makes me wonder if that only works because 2 is the biggest chunk you can take out at once…
Like, if you had n=9 if you'd then n/3=n' and have 3 numbers at the top, but then that would only work if the number isn't prime or comprise of co-primes.
Does it have to be an odd sum? I'll play with it.
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83b459 No.8458
>>8457
With 9 numbers instead of 10
10+11+12+13+14+15+16+17+18=126
add 2 to the previous highest value of the mid-set and work backwards
31+2=33: 33+32+31+30=126
63+63=126
42+42+42=126… actually… it does this for every divisor:
* The factors of 126 are 1,2,3,6,7,9,14,18,21,42,63,126;
But if you were presented with the just the 9 numbers, it looks like you'd take the highest value from the low-set and subtract 1, double the result, and subtract another 1 from that, so:
18-1=17
17*2=34
34-1=33, and work down from there.
Though, I don't know if that holds in the higher ranges.
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83b459 No.8459
>>8458
10+11+12+13+14+15+16+17=108
35+36+37=108 (108/3=36)
54 + 54=108 (108/2=54)
Hmmmmmmrmrmrmrmrmrmrmmmmmmm….
On 3 step polite 126:
41+42+43=126
Midstep is lowest non-2 factor when even?
I need more coffee.
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83b459 No.8460
>>8459
20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37=513/18 (28.5 midpoint)
83+84+85+86+87+88=513/6 (±.5 midpoint)
170+171+172=513/3 (±1 midpoint)
256+257=513/2 (±.5 midpoint)
How to scale a polite number?
pick however many steps you want… like… 6? and then you can produce the politeness
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b129f9 No.8461
Since we can find where c appears as a[t], we can go up one and have c as b[t].
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b129f9 No.8462
Here is a record where a multiple of a appears next to N:
{41:1:52:7:45:61}
This record's coordinates can be calculated from N.
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b129f9 No.8463
This is what occurrences of b[t] = c look like.
c145
{289:1:144:-1:145:145} (289, 1, 0) c = 21025 f = 0
{281:1:142:1:141:145} (281, 1, 1) c = 20445 f = 4
{265:1:140:3:137:145} (265, 1, 2) c = 19865 f = 16
{241:1:138:5:133:145} (241, 1, 3) c = 19285 f = 36
{209:1:136:7:129:145} (209, 1, 4) c = 18705 f = 64
{169:1:134:9:125:145} (169, 1, 5) c = 18125 f = 100
{121:1:132:11:121:145} (121, 1, 6) c = 17545 f = 144
{65:1:130:13:117:145} (65, 1, 7) c = 16965 f = 196
{1:1:128:15:113:145} (1, 1, 8) c = 16385 f = 256
{-71:1:126:17:109:145} (-71, 1, 9) c = 15805 f = 324
{-151:1:124:19:105:145} (-151, 1, 10) c = 15225 f = 400
{-239:1:122:21:101:145} (-239, 1, 11) c = 14645 f = 484
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b129f9 No.8464
CONTEXT – Seeing the Bigger Picture.
CONTEXT – Using ALL of Row One.
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b129f9 No.8467
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b129f9 No.8468
When we've made c into an, what's bn and what's c and how does c increase and is it c+4b? (Depending on what you chose as n)
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b129f9 No.8469
>>8468
Correction: (a-1)b
When you've made c into an, (a-1)b becomes the pattern
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b00cdb No.8471
>>8469
>>8468
>>8470
What do you mean "when you've made c into an"?
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b129f9 No.8472
>>8471
a[1] = c
a[2] = c
a[3] = c
…
The "n is the same thing as a" remark starts to make sense when you realize that c at a[t] functions as an an value and a OR b can be n, since t+a and t+b both have the same factor
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e48742 No.8473
"12.45 - Restate my assumptions."
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e48742 No.8475
" … even when I was mentally disturbed, I had a lot of interest in numbers."
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fd1528 No.8476
>>8433
>Every column that c appears in has what in common?
The first valid n (above 1) in said columns is always prime when c is coprime
c3637 (2, 3, 5 and 7 filtered)
(7258,19)
(7078,3539)
(7018,11)
(6598,3299)
(5158,2579)
(4358,2179)
(4138,2069)
(3674,11)
(2918,1459)
(1798,29)
(874,19)
(218,109)
c6107 (n = 2, 3 and 5 filtered)
(12214,31)
(12178,6089)
(11638,11)
(11314,5657)
(9298,4649)
(8614,59)
(7858,3929)
(5158,2579)
(4114,11)
(2998,1499)
...
When c has three factors, the first valid n in the e=c*2 column is always one of the factors.
c135336263417 (3929*5657*6089)
(270672526834,1)
(270672526834,3929)
c447791149 (13*5657*6089)
(895582298,1)
(895582298,13)
c6380123599 (569*3083*3637)
(12760247198,1)
(12760247198,569)
c240520532961377359853213671 (123323*21279186109*91654346153)
(481041065922754719706427342,1)
...gap...
(481041065922754719706427342,123323)
Not a direct calculation but haven't found any values where the above isn't true yet.
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b00cdb No.8477
Is there anything we can actually do with the gaps aside from them being a stopper for any (e+2n,n) movements? "Not VQC" said "lookup in gaps" but if there aren't any cells we can generate what are we even meant to look at when it comes to the gaps?
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b129f9 No.8478
>>8476
Let's say we have a way to find the first valid n in a column efficiently.
Assuming your assertion is true for all semiprime c, we can make c the product of three primes where the a value that we want is the smallest valid n value by picking the closest prime to d (perhaps by the nextProbablePrime() function in Java), since d > a in a semiprime. Thus, calculating the first valid n value would be equivalent to factoring.
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b129f9 No.8479
Making this prime that is known to be bigger than a as the third factor of c, qc, the a value we want would be the smallest factor of c making the lookup reveal itself more easily.
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b00cdb No.8480
I've updated my program that shows you everything down the factor tree. Instead of just creating a giant text dump, you can tell it what you want to see specifically (so you could just analyze the an cells for example, rather than having to look for them in a giant 6-page wall of text with every other pattern). It'll also work with bigger numbers now (probably not RSA-sized, but if the highest prime factor is maybe 7 digits long it should only take 80 seconds at most - this is because it looks for all ab pairs down the tree). Since we're on 8ch, just so nobody gets paranoid, I'll just put it here using pastebin, but I can put a jar somewhere if anyone wants.
everything.java (contains main) — https://pastebin.com/XfG1SwYN
BigCell.java (also required) — https://pastebin.com/309hK39c
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b00cdb No.8481
The x values in the (e,1) and (f,1) cells where a[t]=BigN and BigN-1 add together to make 2d-1 (so if you took the next cell up (t+1) in one of those you’d get 2d+1 too since x iterates by 2).
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ec6c10 No.8482
I found a link between the 2(x+n)2(x+n) square and the cell in (1,1) where d is equal to the n value from (0,n)'s a=aa b=bb cell. The polite triangle bases from 2(x+n)2(x+n) add together to give the x value in the (1,1) cell. I think you can link it back to the original (x+n)(x+n) with algebra. Once I figure that out I'll post more. This "analyze everything at once" program has already proven to be very useful.
By the way, if anyone's planning on using my program >>8480 here, you'll want to change the subtraction on lines 553, 554, 581 and 582 to an addition (whoops).
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ec6c10 No.8483
>>8482
The x value (which is the 2(x+n)2(x+n) bases added together) is actualy 2(x+n)-1 from the original (e,n) cell. So the x value in the cell in (1,1) where d is the n value from (0,n)'s a=aa b=bb cell is actually also 2(x+n)-1. That's the algebra thing I was talking about.
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ec6c10 No.8484
For even e, the t value in the cell in (e,1) where a[t]=BigN is equal to half the t value of the Root of D cell. For odd e, it's 2t+1.
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81cdd5 No.8485
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81cdd5 No.8486
<Figured I'd get it in while the
>Gettin' it in was good :D
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abe23c No.8487
>>8452
How did you do this?
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02496e No.8488
I noticed this a few days ago, but given the holidays I haven't spent time on it.
Generate the e's for a number, example 259. The odd e's for that 259 appear as a[t] in (e, 1) are:
[517, 509, 493, 469, 437, 397, 349, 293, 229, 157, 77]
I decided to play with them for no specific reason, but I mapped the numbers through a getU function and I got the following:
[258, 254, 246, 234, 218, 198, 174, 146, 114, 78, 38]
What stands out is 146 and 114 (and 78). The Big N for 259 is 114 and the Big Shadow N is 146. I didn't expect this, but I checked with a few other numbers and it seems to hold for those as well. Another thing, 78 is also a value in (3, 259) but belongs to a different chain. Anyone looked into this before? Anyone knows why this seems to occur?
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2c2fb2 No.8489
The x value of the cell in (1,1) where d is the n value from (0,n)'s a=aa b=bb cell is equal to b-a-1 (the b and a from the solution cell, not this cell).
Example:
a=3, b=177, n from (0,n) a=aa b=bb = 15138
(1,1) d=aabbn = (1,1,87) = {1:1:15138:173:14965:15313}, f=-30276, c=229159045, u=87, i=15139, j=174
x from this cell = 173
173=b-a-1=177-3-1
This seems to apply to all cells.
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abe23c No.8490
>>8489
Just in case this wasn't known, I believe that n (0, n where a=aa, b=bb) is equal to 2(x + n)^2.
As for >>8488 I still haven't quite figured this out. It's almost like it is an index for n-values for a given number.
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abe23c No.8491
>>8489
Say we found this cell in (1, 1). Then we do (x + 1)/2 and we got the t for that cell, which happens to also be (b - a)/2 (or x+n)?
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abe23c No.8492
>>8488
I'm still not entirely sure what I'm looking at, I need to think some more about it, but I noticed something.
Big N and shadow Big N seems to always appear as a u for the value of e that c exists in, but the value they exist in also seems to act like a map.
Take 259 for example, it has Big N = 114 and shadow N = 146.
The getU simply calculates the u-value of the numbers, so by doing it in reverse we can do sqrt(8*(114*115/2) + 1) = 229 and sqrt(8(146*147/2) + 1) = 293. The records for these two are:
{4:100:15:14:1:229}
{4:130:17:16:1:293}
The two records for 259 are:
{3:114:16:15:1:259}
{3:146:-16:-17:1:259}
So we can see a method of moving between these records. 100 + 14 (n + x for 229) = 114 and 130+16 = 146 (n + x for 293). This also means we could move across e's and n's on a diagonal (But this does not conserve the c-value).
For example {3:114:16:15:1:259}, we can now move diagonally by doing 114 - 14*15/2 = 9 and 3 + 14*15/2 = 108. That means at e = 108, n = 9 exists. It should be noted that those numbers got my heart to jump. 108 is the smooth number for 259 (114 - 6) and 9 is the x-value of a=7, b=37, but a quick reality check against other numbers slowed it down. This also works moving "up" with n and "down" on the e.
114 + 15 = 129 (e=2)
129 + 14 = 145 (e=1)
145 + 13 = 162 (e=0)
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abe23c No.8493
>>8492
Fyi I wouldn't think of this as what VQC has talked about when he says "diagonally". I'm not sure if it's a fluke, or exists because of how numbers are connected or what, but it allows for navigation / moving around cells.
For example:
You can start at (5, 1, 1) and end up at (0, 8, 1) moving through these records:
{5:1:4:1:3:7}
{4:2:4:2:2:10}
{3:2:2:1:1:7}
{2:3:3:2:1:11}
{1:5:4:3:1:17}
{0:8:5:4:1:25}
I don't know if this movement makes any sense. I might be going down a new rabbit hole that isn't going to span out.
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2c2fb2 No.8494
>>8491
There are a lot of things you can do with the (1,1) cell. VQC said it's the most important cell in the grid at one point. Specific cells in (0,1) and (1,1) with a[t] added to e/2 or (e-1)/2 (depending on parity) give you an and bn, for example.
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2c5b09 No.8495
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4877aa No.8496
Hello Anons!
Anyone got ideas they’re working on?
I’m still working on how square numbers and triangle numbers can be broken down into the polite triangle bases and then reassembled to solve the (x+n)^2 area. We had both successes and failures on the test AA helped me out with.
Thanks btw AA! 
I’m also compiling and running java files now from my Mac terminal, and doing an online java class.
I can edit the files in txt format and then recompile too. It feels fun to learn new skills!
Thanks @everyone for all your work and dedication to this project.
I’m stoked to be here.
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2c2fb2 No.8497
The t value of the (1,1) d=aabbn cell for a=1 b=c is equal to the d value of the (f,1) cell where (e,1) and (f,1)’s polite x values add together to give 2d+1 (I’m not sure if this works for all parities in the same way but it worked for multiple cases).
e.g. c=1427
The cells in (e,1) and (f,1) where x+x=2d+1=75
(-17,1,19) = {-17:1:713:37:676:752}, f=1408, c=508352, u=19, i=714, j=38
(58,1,20) = {58:1:789:38:751:829}, f=-1521, c=622579, u=19, i=790, j=39
[1, 1427]
(1,1) d=aabbn = (1,1,713) = {1:1:1016738:1425:1015313:1018165}, f=-2033476, c=1033756160645, u=713, i=1016739, j=1426
d=713, t=713
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1ea46d No.8498
Here is a tip, if i(t) has not been done before.
Take products, c, that have odd x+n. And even n.
Take one from x+n.
8 triangles.
Create a table.
What does f and 2(n-1) contribute?
Because the tips of all 8 triangles are from (n-1)(n-1) - 1.
Find the pattern from large to small.
There are h families!
Avoid the 13th step of AA.
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1ea46d No.8499
>>8494
Definitely. Plus both it's neighbours.
Check the post count.
Boundary conditions.
Either side.
Proud of you, anons.
It's about Time.
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abe23c No.8500
>>8499
Lovely to see another anonymous poster (Been a while since we've seen you)!
I've been playing with t a[t] = c patterns and I made a few images. Each show the progression of the pattern as more factors are added.
Prime numbers don't have much in the sense of interesting patterns. As you increase the number of factors the interleaving patterns increase.
Note, white is c, black is 1 and the other colors are either prime factors or sub-compositional numbers.
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2c2fb2 No.8501
>>8499
>>8498
You said factoring d and e allows for the factoring of c. I've put together a program that outputs every known and unknown (unless I missed something) down the factor tree. I've been looking for something in a given d and e's unknowns that somehow shows up in c's unknowns but there are so many possible combinations of numbers. Could you maybe give a hint as to where we should be looking, or even just what concepts we should focus on in this context?
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df3148 No.8502
>>8498
Hello Senpai!
>Take products, c, that have odd x+n. And even n.
>Take one from x+n.
>8 triangles.
>Create a table.
I've included an updated sheet soon including f and 2(n-1) and how they contribute to the 8 triangles. PMA and I spent a lot of time working to understand this! This is the lock and key, isn't it? I'm excited to work on this again.
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7f9c68 No.8503
>>8501
You have more than you know. Think logical arrangement of hints, ideas, processes. Efficiencies.
Put them in order.
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7f9c68 No.8504
The Key to All Locks.
https: //en.wikipedia.org/wiki/Goldbach%27s_conjecture
a + b
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81cdd5 No.8505
>>8504
RETURN OF THE TRANGLES!!!
4, 10, and 20 show up, but… that's assuredly a "coincidence", I'd "imagine".
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7f9c68 No.8506
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81cdd5 No.8507
>>8506
you already had me at 47, but at least I finally had my question answered as to "what kinda trangle we lookin' fer whenever we're trangulatin'?" ^_^
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abe23c No.8508
>>8500
I'm guessing this isn't much noteworthy stuff then? Either way, to give some background. Each row of pixels represent column e_t where e is a column where c exists as a[t]. The first row is where a[1] = c, second row is a[2] = c etc.
The color grid represents gcd-value between a[t] and c. So in the first (very tiny) image we have 5 (but the same pattern holds for all primes) while the second is two primes. Black is gcd(a, c) = 1, white is gcd(a, c) = c. The rest are randomly assigned based on gcd(a, c) != 1 / gcd(a, c) != c.
Given 2 primes you have 3 values, a, b and ab (Note this relates to >>7901). For three prime factors you have a, b, c, ab, ac, bc and abc.
The length of the row (width) is equal to c, so each image represents a grid of c * c. The problem, as I see it with regards to this structure is aligning them.
You can also see that it is in reality just 8 triangles, each equal and it generates a square pattern where there are multiple squares depending on the number of factors. Each type of square represents a factor.
What is very neat though is the beauty of the patterns it creates. It's stupidly slow, even when multi threaded and partially generated since it involves so many different values. It could probably be more optimized and my machine isn't the fastest.
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b129f9 No.8509
>>8497
I remember someone mentioning polite numbers in x before
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2c2fb2 No.8510
>>8509
Could you be more specific? Because the only thing I can think of that has anything to do with polite numbers and x is the thing I did in the post you're replying to.
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81cdd5 No.8511
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b129f9 No.8512
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2c2fb2 No.8513
>>8512
…that's what I did in the post you replied to.
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b129f9 No.8514
>>8513
Looks like the hint's role is being revealed then. I wonder how the others can be revealed
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2c2fb2 No.8515
>>8514
You might be onto something. I've checked with most c values where d=23 and it appears that for most of them the t value for one of the unknown (1,1) cells appears as a d value in either (e,1) or (f,1). I think a few of them didn't but I forgot which, and I also didn't check what happened when you added the x values together. I've look into it properly and report back later.
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2c2fb2 No.8516
Turns out the t value of the (1,1) cell where d is the n value from (0,n)'s a=aa b=bb cell was actually j or (x+n) all along. I don't know if anyone figured that out already. (1,1,j)'s d value is the n value from (0,n)'s a=aa b=bb cell. It also appears that j turns up as a d value in (e,1) or (f,1) sometimes. I'm just looking into it some more.
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2c2fb2 No.8517
>>8516
And the j of that (1,1) cell is 2j. So if we're looking for (x+n)(x+n), we'll find 2(x+n)^2 in (1,1) at (1,1,(x+n)).
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Post last edited at
2c2fb2 No.8518
>>8514
I looked at all of the odd c values with a d of 23 (529 to 575). I took the t value of the cell in (1,1) where d is equal to the n in (0,n)’s a=aa b=bb cell, and tried to find it as a d value in either (e,1) or (f,1).
Every time you have a=1 b=c, t from (1,1) shows up as d in (e,1) and (f,1).
Example:
c575 = (46,265,12) = {46:265:23:22:1:575}, the relevant (1,1) cell is (1,1,287), and 287 appears as d in (46,1,12) and (-1,1,12). This works for all a=1 b=c.
For solution cells, it gets a bit weird. t for at least one of the relevant (1,1) cells (so solution j or solution (x+n)) appears as a d value in (e,1) for most of them. I didn't notice anything in particular that could be used to calculate this cell, but it's a possibility.
Some of them (c535, c551, c575, c567) have it turn up in (f,1).
Occasionally (c539, c549), the t value of the cell in (0,1) where a is equal to the n value from (0,n)’s a=aa b=bb cell (which is actually the t value we were already looking for plus 1) appears as a d value in (e-1,1).
Some of them (c543, c545, c565, c573) just don’t turn up. Who knows why.
So while j definitely turns up as a d value in (e,1) quite often, it doesn't seem to follow any stable patterns, considering it just kinda doesn't happen sometimes.
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341dcd No.8520
>>8499
Hmmm. (1,1) is one of the most important cells. So I started there looking for patterns. Interesting find for a *b values moving diagonally in the Grid from (1,1). Found the following combos:
(4,4) a * an
(9,9) BigN * c
(25,25) an * c
(49,49) a * c
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79af72 No.8521
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81cdd5 No.8522
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b129f9 No.8523
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1c551a No.8524
So, I've been working on this for a while trying to attack it from different angles. I've identified a couple of rules governing the factoring of numbers, Im not sure if this is new stuff or not… For every number (except for the square of every second even number) has a perfect square number larger than it that when subtracted from that larger perfect square number results in a smaller perfect square. The root of that larger perfect square is always the average of the sum of the factors of the starting number. The root of the smaller perfect square is always the distance between the average of the factors and the factors themselves.
For instance:
7 *11 = 77
7+11=18
18/2=9
9*9=81
81-77= 4
9-2=7
9+2=11
This works with all odd numbers and every other even number. And it also always seems to work with any number that is the product of two primes.
Unfortunately, its just as hard to predict the average of the two factors as it is to predict the factors themselves. But, I noticed something else:
For almost every number there is only 1 larger number that is 1) a perfect square and 2) the difference between the two is also a perfect square. So, I've been thinking that since every subsequent square number is the root of the next lower square * 2 +1… I think it should be possible to plot an intercept course.
Sort of like the old 'police pursuit' physics problem but with the diffence being, the two cars travel a constant speed, and the distance "between stops" is what changes. Going off of the example of 77 above, car 1 starts at 77, car 2 starts at 0. If they travel the same speed and only stop at square numbers then the next time they stop at the same time is when car 1 is at 81 and car 2 is at 4.
TLDR; is there a formula that could be used to plot an intercept course where speed is constant, the 2 objects in motion make stops where the distance between stops increases by a known variable and the point of interception is when they both stop at the same time?
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388050 No.8525
>>8524
So you've started looking at it two-dimensionally?
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47d6d1 No.8526
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99b9ab No.8527
>>8526
I can't speak for anyone else, but I'm still working on it. My spare time has been eaten up for a while, so things are moving slower.
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2c2fb2 No.8528
>>8526
It was destined to stagnate a bit at least. There are still daily conversations on Discord. The board isn't dead but obviously when all we have to go on is metaphors and vagueness it gets a bit difficult.
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81cdd5 No.8529
>>8526
>>8527
>>8528
It's my bad.
I've been slacking on poking the nerds to post m0ar often on the bread.
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b129f9 No.8530
I should have known the unified field theory would be subject to this..
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81cdd5 No.8531
>>8530
It's almost as if we've talked before…
Weeeeeird.
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cad7bb No.8532
When you all are done, since SSL is moot, you'll have yourselves one sweet login database at HIBP Password Verifier.
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81cdd5 No.8533
>Be God
>Have a child in mind.
>Only one man at a specific time can produce the one specific sperm that will make that child a thing.
>Put/encrypt that specific child into a woman
sperm-small prime
unfertilized egg-large prime
fertilized egg-semiprime
Gestation-same process for every RSA situation.
Birth-The child/packet/message/file/whatever
Cutting the umbilical cord - Going from .999… to 1 (e?)
First Breaths - Priceless.
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349a57 No.8535
In column 1 row 1 at x = c (for odd c) a-1 and d represent something, but is it of any use?
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b30a9a No.8536
which means sqrt(a) is our long side length of the triangle, with t and t + 1 being the other two sides.
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291f8b No.8538
Damn my intuition bells are going off right now Lads! What I’ve found in using my method is that when you begin building up the factors of the (x+n)^2 -1 area, you first arrive at a perfect square that is a potential match for Potential x+n or P(x+n). D, e, and f all determine what the first perfect square will be, and then
The big idea is finding the first perfect square built using the root of f.
And then using multiples of it.
F limits the possible correct values.
It’s a 2 step process. All larger x+n values can be built from the first perfect square.
Once you find the first perfect square, the other possible values are just multiples.
So PTB for x+n=6889 = 2(sqrt ((f-1)/8))-1 = 7
First match is 7 * 5 +1 = 36
Sqrt(36) = 6 = potential x+n
Here's the perfect square creation I'm talking about. This is building the x+n square using 4 rectangles (or 8 triangles) +1
Step 1: find the first perfect square.
PTB = 7
7 * 5 +1 = 36
potential triangle base value(u) is 6
potential triangle side value (u-1) is (6-1)=5
Step 2: correct x+n is a multiple of the correct value above ^^^
Formula is: u * (u-1) * 4 +1 = potential x+n
1. 6 * 5 *4 +1 = 121, sqrt(121)=11
2. 12 * 11 * 4 +1 = 529, sqrt(529)=23
3. 18 * 17 * 4 +1 = 1225, sqrt(1225)=35
4. 24 * 23 * 4 +1=2209, sqrt(2209)=47
5. 30 * 29 * 4 +1= 3481, sqrt(3481)=59
6. 36 * 35 * 4 +1= 5041, sqrt(5041)=71
7. 42 * 41 * 4 +1= 6889, sqrt(6889)=83 = correct x+n value
Step 3: use the quadratic to check/verify each iteration above ^^^ resulting in an integer answer (no remainder)
Sqrt(c + (x+n))-d = n
I'll run it on some more c values, I know this is c6107.
Just trying to find an idea that makes sense first, and then test it out.
Pretty cool to do this from memory with a calculator and pad. I love this problem. I think about it in the morning when I wake up, and it pops into my mind during the work day. I haven't posted much lately bc I had nothing new, but maybe this idea is worth exploring.
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0bee42 No.8539
Many are the plans in the mind of a man, but it is the purpose of the Lord that will stand.
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5ff613 No.8540
>>8536
But does this help with out problem at hand?
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5ff613 No.8541
>>8540
Ugh, with our problem at hand. It's still early in the morning.
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566843 No.8546
>>8526
I still lurk. I got sidetracked during the holidays. Still do work on this though. Noticed something recently. thanks to
>>8535
I was looking at (1,1).
In (1,1) the values for x and a are tied to a pythagorean triple,
(x, a-1, a) so that a*a = x*x + (a-1)*(a-1). Then I couldn't really follow what d was getting to, but I think this might be a way to tie together unrelated squares, because x*x, a*a, (a-1)*(a-1), d*d, are all related to eachother in some way in these equations. Granted there isn't much but forgive me.
Another thing I saw is that if you look at the records in row 1, all of their 'ones' place values repeat over time, no matter what base you are using. For instance, if we have a base equal to 45, then all of the values in column A % 45 will repeat over time. For instance, if we use base 60, then for every even e, the a's repeat every 30, then if we use an odd e, it repeats every 15. Hovever, if our base is odd, it will always repeat at that interval. Also within the repeating the same pattern occurs backwards so theres half as many options.
For base divisible by 4:
Even e:
A[t] % base = A[t+base/4] % base
Odd e:
A[t] % base = A[t+base/2] % base
Base divisible by 2:
A[t] % base = A[t+base/2] % base
Other base:
A[t] % base = A[t+base] % base
We could then iterate through the first t records in (e,1) because those would have the correct a%t values,
then maybe we could use modular arithmetic to solve it from there. Maybe mix in the -f entry to get two equations. Maybe deliberately use a base that is divisible by 4 so that d will be even and -f will be odd, and you'll have two different bases to use in the modular equation.
Lets use base 60 for c=145
We know that A[t] = na for some value in (1,1), and that the values A[t]%60 for this are pic related:
(1, 5, 13, 25, 41, 1, 25, 53, 25, 1, 41, 25,13,5,1,1,5,13,…)
We calculated all of these and there are a bunch of repeats so we filter them out
now our options are na == 1, 5, 13, 25, 41, 53 (mod 60)
Second pic related is -24.
If we look at (-24, 1) = (-f, 1), then there is an A[t] = n(a-1).
Now all the options are :
(6, 20, 38, 00, 26, 56, 30, 8, 50, 36, 26, 20, 18, 20, 26, 36, 50, 08, …
which can be reduced to n(a-1) == 6, 8, 18, 20, 26, 36, 38, 50, 56
We can check every permutation which would be 6*9 attempts = 54 iterations, and each time you'd do this.
Lets say I'm testing n(a-1) == 18, and na == 41 (mod 60)
na - n(a-1) == 41 - 18 (mod 60)
na - na + n == 23 (mod 60)
n == 23 (mod 60)
So I guess it would always turn out to be just getting the difference of all these numbers, which isn't too intense of a calculation. Of course once we get n (mod 60) it's not like we have n or anything. We might be able to narrow it down further with other equations and known variables but idk. Just thought this was neat and wasn't sure if anyone else had posted it.
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81cdd5 No.8547
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81cdd5 No.8550
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8a69d0 No.8552
>>7747
We've been trying to figure out the Parabola or perhaps, promulgation of rounding errors, for over a year now. Anyone figure it out?
Also, is Chris OK?
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89ec56 No.8553
It's all just one guy.
It's all just one guy.
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89ec56 No.8554
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27241f No.8555
>>8554
I like the way you higlighted specific cells but made the resolution of the picture low enough that you can't actually see the numbers. Nice touch, that.
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81cdd5 No.8556
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27241f No.8557
>>8556
I was being sarcastic. You could apply the colour thing to any set of numbers so it doesn't really matter. It looks like this is for 5x31. It doesn't really add any new information aside from highlighting (-1,n). We were already told to do that, but when I looked into (-1,n) I didn't find any unique patterns that changed anything, and it had the same patterns as the other negative square columns ((-4,n), (-9,n), etc). We were already told to do that colour diagram thing too, early last year. He said that the colours were significant. The only other time he used these same colours was in his triangle diagrams, but I don't remember being able to find any useful connections personally (plus nobody found anything originally (GA made some example diagrams but I don't remember which thread this was)).
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81cdd5 No.8558
>>8557
So you can explain 3 black segments, one gray segment, 2yellow highlights, the green segments, the purple segments, the 2 same-purple highlights separating green segments, and the 2 blue highlights?
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01587d No.8559
2d(n-1)+f-1= 2xn+ x^2
F and d limit possible n and (n-1) values.
Let’s work on this!
Is it a graph line where only certain integers work?
More about eliminating values than solving?
The algorithm is ancient.
According to VQC
How to combine multiple variable equations to run side by side.
a new form of algebraic solution
Underlying fractal patterns
Triangles and squares
And how they combine
Limiting possibilities
Factors contained within f.
(D+n)^2 - (x+n)^2=c
Simple and clean.
So much complexity and simplicity combined.
Mods and patterns
(Of mods)
Factoring each square
Multiple possibilities for perfect squares in (x+n)^2
Geometric patterns in the Grid
Geometric patterns in the 8Tu+1
Leading to a Grid shortcut based on understanding of the geometric patterns.
How do we factor the two squares (d+n)^2 and (x+n)^2 ?
Using only c d e f ?
I'm reworking equations over here.
I have too much time invested here to give up.
And I'll keep going till we solve this shit.
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81cdd5 No.8560
I bet these folks would SUPER appreciate it/be terrified if someone were to open that wallet up and give everyone their $190 million back…
https://www.marketwatch.com/story/crypto-exchange-customers-cant-access-190-million-after-ceo-dies-with-sole-password-2019-02-04
Crypto exchange customers can’t access $190 million after CEO dies with sole password
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566843 No.8561
>>8557
That was a tkinter app I made that would do it for any records. Never found much from it. Then again I never really used it because I saw the flaws and I made a better app. I think we could use the coloring to highlight these cells but then view them from a different perspective. I'm stil working on a program that will let us view the cells from any angle. AKA originally the axes are (e,n) but I'm trying to make something that will enable use to view from any axes and highlight any cells.
>>8559
>using only c d e f
I think that this could be the key. He probably chose those letters for a certain reason. Maybe theres a bunch of steps. c gives you d, d and c give you e, d and e give you f, f and e give you g, g and f give you h, …. up until 'n' I'd guess.
c d e f g h i j k l m n -> finally -> a or b
>VQC: Twelve steps are the key
c -> n is 12 steps if we follow this pattern. Now obviously I have no idea what these steps are in specific, but if this is the case then vqc has given us up to f. This is 1/3 of the way already.
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befb45 No.8562
>>8526
Still lurking here. Still my favorite board of all time. -Hobo
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81cdd5 No.8563
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2b6a32 No.8564
>>8561
We do have this one: >>8498 stating there are h families. So c gives d, c and d gives e. d and e gives f, f and e gives g? Then g and e gives h?
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4d8219 No.8566
Topol, here's one of yours!
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99b34d No.8570
Let's fill this one up, lads. When that's done, Fresh Bread is ready. Maybe we'll start kicking ass again??
>>8567
>>8567
>>8567
>>8567
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341dcd No.8571
I just noticed a cool pattern.
Starting at the (na transform) element,
a[t] (e) - a[t] (-f) = an increasing pattern.
128-127=1
100-97=3
76-71=5
56-49=7 which is (n-1)
So the difference between a[t] (e,1) compared to a[t] (-f,1) moves upward in an ascending pattern until the first element in a given e column.
for odd e, (e+1)/2 = a[1]
So this info greatly limits our search area.
Thinking out loud over here.
We limit the search using the (na transform) element and the a[1] element.
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341dcd No.8572
>>8571
To be clear, I’m not suggesting iterating by x.
I’m suggesting using every available piece of info to limit the search area.
BigN is also a limiting piece of info
Along with 2(sqrt((f-1)/8)-1
Set boundaries, then factor
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341dcd No.8573
More patterns.
This one has (-f,1) a[t]=c and its equivalent element in (e,1) is distance of (a) apart, 287 - 270= 7 = correct a value
Also, the a[t] = (bn) value = 328
in (e,1) 328 - 287 = 41 = b
so c, a, and b are available/calculable in a triangle pattern right next to each other in adjacent elements.
Here's a diagram.
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341dcd No.8574
Once you c it you can’t un-c it?? Why does a[t]=c appear in many of our cases?
for c287
2(sqrt(d))-1 = 7 = (n-1)
Must be a fluke, but still analyzing for patterns over here.
Lol, for c6107 2(sqrt(d))-1= 15 and correct (n-1)=35
Shared factor of 5. Interesting.
and 2(sqrt((f-1)/8)-1 = 7 which is another factor for 35
Hello PMA, Jan, and 5DAnon can I please request your assistance?
Could it be a characteristic of ONLY semiprime c values that we always have one a[t]=c element?
Makes sense that c always appears at a[t] since the prime factors have to show up again.
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341dcd No.8575
>>8574
And if that element exists for a given semiprime c, we can solve the problem with the adjacent elements. (maybe!)
You guys know how I work, calculator in hand with a pencil at the ready. If the idea sucks, that's fine. Working from small examples over here.
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344e49 No.8576
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349a57 No.8578
>>8576
So we have till 3rd of march to figure this out.
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344e49 No.8579
>>8578
I wouldn't hold my breath if I were you. How many times has he said "hey guys let's go through the solution right now/tomorrow/next week" and then acts like he never said that? And if he actually goes through with it this time, keep in mind, there are people who have been following along with this board for months if not more than a year who don't even understand it so if he legitimately goes through the solution (or "part 1", whatever that means) nobody will even know what the fuck he's talking about aside from maybe 5 or 6 of us who have put significant effort in already.
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344e49 No.8580
VQC, we know you've been posting on /qresearch/ with your name again. Why not come back here and say hi?
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74d41f No.8581
>>8580
VQC - I agree with AA, you should stop by and say hello.
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81cdd5 No.8582
>>8580
>>8581
Y'all are "special" if you think he wouldn't come back with:
"We never left.
It's time to return publicly.
VQC"
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258a51 No.8583
>>8580
Got any post ids for those? I know he also sometimes post hints there when people fish.
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81cdd5 No.8584
>>8583
I've heard that somewhere, too… Firsttimeposteranon47
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344e49 No.8585
In columns where e is a square, c is the sum of two squares. We already know this. What hasn't been pointed out is that in columns where e is a trianglular number, c is the sum of a square and a triangle. This could potentially be useful given some of the things that Chris has been saying on /qresearch/ recently (speaking of which, Topol, you should post all of those screenshots here rather than just putting them on Discord).
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Post last edited at
026429 No.8586
>>8585
Yeah Topol, share the screenshots for those of us who don't hang out on discord.
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b69141 No.8587
aan(n-1) rings a bell with all these new posts.
Supposedly this type of integer is easy to spot.
Although we haven't discovered the identification process.
Lol.
product of triangles and squares, i think.
Best idea I can think of is to find the next largest perfect square, which should be (aann)
Subtract the difference of (aann) and aan(n-1)
For c145 it's 625-500 = 125
Then, aan(n-1) / 125 = 500 / 125 = 4 = (n-1)
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b69141 No.8588
>>8587
Above is a small example, but here is another key idea we have yet to solve.
aan(n-1) is supposed to be easy to spot when comparing (-f,1) and (e,1) a[t] values.
We worked for a week on this, and we need to finish it, as Saga correctly pointed out yesterday.
We fucking work our asses off on an idea, then bail on it when VQC distracts us with a new idea. That distracting faggot.
He's doing it on purpose to slow us down.
Let’s make a list of unsolved crumbs.
And then work on them independently, while sharing our results. That would work well for us as a group. We are all very independent souls but love to check out each other's ideas.
And we share a common purpose, to do our part for Q / VQC etc. and our fellow humans worldwide.
Thoughts, fellow Anons and Math Fam?
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b69141 No.8589
>>8567
Let's fill this bread up with some excellent posts about unsolved crumbs to work on. Then, we can move to our new bread.
>>8567
>>>8567
>>8567
>>>8567
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b69141 No.8590
The easiest method I can think of is this:
Get the (e na transform) and (-f na transform) elements.
Then create the list of a[t] values for both columns up to a[1].
Then simply move up subtracting e a[t] from -f a[t] and divide c by each result.
First whole integer result is prime a
It could be millions and millions of calcs, but it will run super fast, bc it’s so simple.
(e,1) gives us all factors.
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81cdd5 No.8591
>>8586
But that takes eeeeeeffooooooooort!
fiiiiiiiiiine
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2344ac No.8593
an interesting property, admitedly tested only on short integers
not directly connected to the problem presented, but nevertheless
sum of digits in base(b+1) is same as last digit in base(b)
e.g (base8):
0c1420=1+4+2+0=7(in base8) means its divisible by 8 and 7
0c3774=3+7+7+4=7(in base8) means its divisible by 7 and remainder when dividing by 8 is 4
0c7120=7+1+2+0=3(in base8) means its divisible by 8 and remainder when dividing by 7 is 3
0c6305=6+4+0+4=7(in base8) means its divisible by 7 and remainder when dividing by 8 is 5
0c6620=6+6+2+0=7(in base8) means its divisible by 8 and 7
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349a57 No.8594
>>8591
Hehe, the x^1 = d … x^(d-1) = d wasn't VQC, it was me. I was fishing for him and playing with the idea of roots of david being related to the roots of unity.
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81cdd5 No.8595
>>8594
-shrug-
The interaction got VQC's attention for the crumbs.
Fixed.
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81cdd5 No.8596
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344e49 No.8599
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344e49 No.8600
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344e49 No.8601
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