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/vqc/ - Virtual Quantum Computer

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File: b2fa1be23dd8c4c⋯.jpg (136.44 KB,1280x800,8:5,atomy.jpg)

File: 29462fab34f1044⋯.jpg (73.87 KB,1600x900,16:9,równanie.jpg)

File: 9a6bed46e1ac495⋯.png (24.09 KB,718x253,718:253,E-1-Factorization.png)

File: 891ec07bd6fb111⋯.jpg (36.84 KB,299x400,299:400,Pierre-de-Fermat.jpg)

File: 211aee91b054fa2⋯.jpg (38.76 KB,700x360,35:18,pierre-de-fermat-42649.jpg)

2dbaf3 No.2555 [View All]

Virtual Quantum Computer

Definition

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 be able to factorize large semiprimes, all the way into the hundreds of digits, which would break the RSA cryptosystem.

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.

Variables

The map's legend is {e:n:d:x:a:b}, where d is the result of removing the largest square from c AKA the square root,

e is the remainder,

n is what you add to d to be exactly halfway between a and b,

and x is what you add to a to make d.

c is any number that is the difference of two squares, so odd numbers are included. It is the number you want to factor.

f is what you add to c to make a square.

t is the third coordinate in the VQC..

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.

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-group.

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.

The x-intercept of the line that goes through the point containing the factors of c is (a + 1).

(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)

(e, 1) = the genesis cell.

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.

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 = the difference between the square root d and the larger of the two squares

n = ((a + b) / 2) - d

d + n = number that is exactly halfway between a and b

d + n = i

x = d - a

x = (floor_sqrt(( (d+n)*(d+n) - c))) - n

x + n = j

f = e - 2d + 1

t = the variable that lets you traverse the infinite elements in for a given (e, n) that has values.

if (e is even) t = (x + 2) / 2

if (e is odd) t = (x + 1) / 2

701 posts and 201 image replies omitted. Click [Open thread] to view. ____________________________
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4d8060 No.3333

>>3332

>all for a LARP right?

Q—

Is elevating somebody curious enough to click on a typical larp thread to that of warrior for truth and justice not the most kindest act in written history?

VQC—

Is elevating somebody curious enough to click on a larp within a larp to somebody destined to upheave 50 years of number theory and cryptography not a kind act?

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4d8060 No.3334

File: 117eb1984a907b0⋯.jpg (22.98 KB,418x294,209:147,lp4f324bd1.jpg)

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ff4dbe No.3335

>>3331

>Why are people like you more qualified to solve this problem than mathematicians?

We aren't all autistic by the way.

>(0,n) one row to rule them all

>x marks the spot

>the square in 0,1 is the basis for all patterns in n=1

So you're saying the solution has something to do with these posts?

>>3310

>>3311

Or are you saying something else (because nobody replied to those posts with anything)?

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ff4dbe No.3336

I'm looking at the 0 column and the relationship between c and c^2. I found a few weird things. For the square of a semiprime (probably every square but I'm only paying attention to that table of squared semiprimes), for (a, b) = (1, c^2), which will always be the first cell of the infinite set, t increases by the same number throughout the infinite set (e.g. 11, 21, 31, 41, 51, always +10, but that 10 changes set to set), a is the list of squares from 1 to infinity (the same 1, 4, 9, 16 each time in every set), b increases by a linearly increasing amount (e.g. 441, 484, 529, 576, 625, so it's +43, +45, +47, +49 etc), d also increases by a linearly increasing amount (e.g. 21, 44, 69, 96, 125, so it's +23, +25, +27, +29 etc), and x is linear with a gradient somehow related to t (e.g. 20, 40, 60, 80, 100, which is a gradient of t's increase * 2). Obviously e and n stay the same (0, 200) as you'll see in that table. The example I used for those numbers was c^2 = 441, c = 21.

Here's another example with c^2 = 225, c = 15. (e, n) = (0, 98). t is 8, 15, 22, 29 (+7 each time), a is 1, 4, 9, 16 etc like before, b is 225, 256, 289, 324, 361 (+31, +33, +35, +37), d is 15, 32, 51, 72, 95 (+17, +19, +21, +23), and x is 14, 28, 42, 56 etc (linear with a gradient of t's increase * 1 instead of *2 for some reason).

What that means is, if we use c^2 as our c, every variable follows a predictible pattern, although I don't know why each of the numbers starts where they are. Maybe it has something in common with (1, c). I looked at the (1, c) cells for c = 21 and c = 15 but the relationships are pretty weird and I can't figure out how they work or how they relate to their corresponding c^2 cell, but there's bound to be at least one if not several relationships there. It might just be how late early it is right now but I really hope someone else looks at this and finds something, because it definitely seems like an important relationship and Chris seems to have alluded to it.

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4cf7a6 No.3337

File: 33d48c56d5da5cc⋯.jpg (49.8 KB,500x495,100:99,dfjkfdkjdf.jpg)

File: ea2ae0715f8610b⋯.jpg (489.3 KB,2000x2563,2000:2563,59508.jpg)

File: 71d55302f807209⋯.jpg (41.82 KB,517x270,517:270,William-Kingdon-Clifford-Q….jpg)

File: 928d1fc82bba5fc⋯.jpg (60.68 KB,500x250,2:1,CliffordWilliam-Testing500….jpg)

>>3299

>…for each extension of these variables you'd need a separate dimension of the grid, though,…

Have been seeing this as well. Appears the additional 'dimensions' are related to derivatives (rates of change, how the variables GROW), or second derivatives, sometimes interleaved. These are associated with the integer 'points' in the grid.

Gut and some research seems to be pointing toward a Clifford Algebra associated or overlayed on the grid. When we have those vectors for two points of interest, some inner product or other transformation would lead to a solution. Have been interested in learning about Clifford Algebra for a while as a foray into next level math understanding. Also, there were some suggestions earlier by Chris to dig into in the meantime, and the digging keeps turning up Clifford Algebra (will have to sauce that later).

Baker, we're over 700 posts. Can we consider including Cliff in the next bread, to complement Fermat in RSA#8? Some interesting stories, twists and turns in mathematics / physics, resurgence in his work decades later, and likely has a bearing on where we're headed. Touches on roots, modular number systems, quaternions, etc. It gets at the geometrization

of the real number system. Plus he wore an epic beard.

Some quotes from William Kingdon Clifford (they read like an anon credo!):

https:/ /libquotes.com/william-kingdon-clifford

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4cf7a6 No.3338

File: 76f6a11799d7d29⋯.jpg (93.08 KB,1200x630,40:21,william-kingdon-clifford-q….jpg)

>>3333

Checked!

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12909e No.3339

>>3330

def factor(number):

C = number

A = 1

B = C

D = int(math.sqrt(C))

#print(D)

E = C - D*D

X = D - A

N = int((X*X+E)//2)

newX = E%2

newD = int((newX*(newX+2)+E)/2)

newA = newD - newX

while(gcd(newD-D,newA) == 1):

newX += 2

newD = int((newX*(newX+2)+E)/2)

newA = newD - newX

newA = D - newX

return newA

Here is my code for this. I've noticed that if you set D=1, then returned value is the negative factor of C (so with real D you get factor a, but with D=1 you get factor -a), so you don't even really need to calculate D, but it's here anyway. I can't factor RSA because (int((newX*(newX+2)+E)/2)) is too large for a float and it won't divide but I'm very confident that this works. I've tested it for some products of 2 primes (like 4 digits) and it has worked every time.

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12909e No.3340

File: 1ad95032db3ad29⋯.png (53.23 KB,404x492,101:123,Screen Shot 2018-01-25 at ….png)

>>3339

Here is output that semi-confirms it

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12909e No.3341

>>3340

>>3339

Also this was me I forgot my trip.

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5167b5 No.3342

Has anyone noticed this before?

(0, 5). Divide the a's by 5 and you'll get (1, 1) d's.

{0:5:20:10:10:40}

{0:5:60:20:40:90}

{0:5:120:30:90:160}

{0:5:200:40:160:250}

{0:5:300:50:250:360}

{0:5:420:60:360:490}

>>> 10/5

2.0

>>> 40/5

8.0

>>> 90/5

18.0

>>> 160/5

32.0

>>> 250/5

50.0

>>> 360/5

72.0

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5167b5 No.3343

>>3342

And the a's for (0, 4) is also equal to the d's of (1, 1)

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4cf7a6 No.3344

File: 3a16321990e1806⋯.png (53.73 KB,1221x575,1221:575,n=0_n=1_neg_e_squares.png)

File: 6ad650c377e37e6⋯.png (41.65 KB,752x644,188:161,n0_transform_examples.png)

File: f58cc60a842e327⋯.png (51.43 KB,751x621,751:621,n0_transform_d_and_c_break….png)

>>3288

>>3282

Thanks anon, this was an interesting dive, only part way through understanding (haven't dug into patterns at n=1).

>>3290

>But how is this a solution when the a and b values are still unknown?

>What am I missing?

Don't think you're missing anything, and not sure yet either, but useful for a quick jump to n=0 or n=1.

It also produces a new e that is a perfect square. The new t is always an integer that is the square root of the negative of the new e. This is expected because we know:

e=2an-x^2, and if n=0, e=-x^2

I think being able to transform to a perfect square column in the -e space may be useful once everything is worked out. There is a subsequent transform of 'a' needed, as illustrated below.

Attached images relevant.

First is the orig VQC, generated by Teach back in Dec and on pastebin. Showing only the -e perfect square columns, for n=0 and n=1. The gray bar is the first record, passing through {0:0:1:0:1:1}. Added x's starting at e=-9 above bar, as a sequence for 'a' could be extended upward with decreasing a values (moving t through zero to negative?).

Note: at n=0: d, a, and b increment by 1 for each t. x never changes. x^2=-e. There is a gap between a and b, which is 2*x, and this never changes for t sequences. Also, d-x=a for any n=0.

Note: observe how d increases as we move leftward decreasing e (each +1 increase in x). It's not linear.

seq:1,2,3,5,9,13,19,25,33

See: https:/ /oeis.org/A085913

A085913: Group the natural numbers such that the product of the terms of the n-th group is divisible by n!. (1),(2),(3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),… Sequence contains the first term of every group.

1, 2, 3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, 969, 1013, 1059, 1105, 1153, 1201, 1251, 1301, 1353, 1405

There is a similar (same initially) sequence

See: https:/ /oeis.org/A099392

A099392: a(n) = floor((n^2-2*n+3)/2).

1, 1, 3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, 969, 1013, 1059, 1105, 1153, 1201, 1251, 1301, 1353, 1405

The second formula was easier in excel, but it breaks down at x=54. The d, a, b, and c get out of sync, and no longer check out (see highlighted region in screen cap). Maybe that's why the oeis.org sequence ends there? Maybe the A085913 sequence based on the factorial and groups would continue to work? Not sure, but this doesn't scale at this point for d, using this quick excel model.

- also highlighted in that image is e=-1849, the transform for 87 (1x87) to n=0: {-1849:0:44:43:1:87}, if anyone wants to find a link to the 87 (3x29) record transformed to n=0: {-169:0:16:13:3:29}

Ok, here are transformation examples with a few of the 'known' factors we've been using. Doesn't apply to getting from the 1*c to desired a*b factors yet, but interesting patterns. Refer to image with A085913 in top left, starting at e=0.

Take 85 (5x17)

{4:2:9:4:5:17}

transformed to n=0 is:

{-36:0:11:6:5:17}

Calc d for t=1 at x=6 is 19 (highlighted tan), and we want d=11, so transform 8 steps. a and b are 13 and 25, so taking away 8 from each is 5 and 17, 5x17=85, check.

87 (3x29)

{6:7:9:6:3:29}

to

{-169:0:16:13:3:29}

Calc d for t=1 at x=13 is 85 (highlighted tan), and we want d=16, so transform 69 steps. a and b are 72 and 98, so taking away 69 from each is 3 and 29, 3x29=87, check.

145 (5x29)

{1:5:12:7:5:29}

to

{-144:0:17:12:5:29}

Calc d for t=1 at d=12 is 73 (highlighted tan), and we want d=17, so transform 56 steps. a and b are 61 and 85, so taking away 56 from each is 5 and 29, 5x29=145, check.

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4cf7a6 No.3345

File: 6737c9b3d16320e⋯.png (15.7 KB,590x222,295:111,e1n5-interleavePattern.png)

File: bf2a9171f7e8532⋯.png (493.47 KB,1259x800,1259:800,visualizing-fermats-last-t….png)

>>3339

>>3340

>>3341

Looks very interesting CA! Will have to dig into that when some time frees up, maybe you've got this!!!

>>3342

>>3343

Have been enjoying the patterns you point out Isee. Those are indeed interesting.

- also, some of the patterns PMA has pointed out with delta d's, and interleaved second differentials I see as well.

- for example, (1:5) attached pic.

- I'll throw a post together with some other patterns done visually.

Also, check out the interesting patterns when visualizing Fermat's last theorem, screen capped from a tube. I think this is what we have going on in a way.

>>3331

>… LOOK AT HOW CLOSE TO WINNING WE ARE!

Ok, but how do you KNOW we are close to winning?? Anything more to share?

> Reread Chris crumbs!

Yes, still working through them, picked this up a couple weeks ago to actually work through stuff (where Teach and all were at mid Dec). Each crumb leads to a deeper understanding of the VQC/GRID. One of the things that keeps me going on this, LARP or not, is that Chris has always been coherent in his crumbs. Granted, we could start dropping some crumbs with the grid now, even without an end solution, but it sides more with an 'informed faith' rather than a 'blind faith' at this point.

- we just need to convince Chris that a) we're ready for the next walk-through tutorial session, and b) it's Time for that Now to get ready for next phase of bigger picture! (hint hint Chris).

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4cf7a6 No.3346

File: 4ef74883255aa68⋯.png (23.83 KB,976x685,976:685,VQC-Grid-CSVexcel-map.png)

File: e1ff87df9b89adf⋯.png (25.33 KB,945x694,945:694,VQC-Grid-Shaded.png)

File: 0aa28685924d8d0⋯.png (20.34 KB,2120x1632,265:204,book1-negE.png)

File: 36c7444f2864a29⋯.png (20.63 KB,2120x1632,265:204,book1-posE.png)

File: 93deeb183dfe27d⋯.jpg (35.92 KB,612x447,204:149,472338615.jpg)

Ok, here are a few playful images / exploration of patterns. Follows along with the fermat visualization above.

First, I took the orig grid output, e-64 to e64, t=1 to 10, n=0 to 63.

Zoomed out, you can see patterns right away.

Added darker shading to the cells with values. Some ranges only have a few t's, as the d, a or b capped out and stopped generation, but they would go on.

Wouldn't quite print right, so generated a png output for the left side and right side of the grid.

Could play in an image program, but chose to print these out, and play on a light table.

I see 2 parts to our goal: 1) be able to hop/transform to another cell that is valid (not empty), and b) able to go in proper direction(s) and transform appropriately along the way. Ala hopping the lilypads on the grid-pond.

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12909e No.3347

File: b20764388ff8396⋯.gif (1.5 MB,1000x600,5:3,XGrids.gif)

File: 535369125d302ce⋯.gif (13.62 MB,1200x1000,6:5,DGrid.gif)

>>3346

I'm pretty sure these can be explained by looking at the D and X grids.

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769a5e No.3348

File: 89fdca0fd65ad1e⋯.png (754.84 KB,2374x1895,2374:1895,c145_dt_diff_at_f.PNG)

File: fc674071eb67e61⋯.png (392.65 KB,2699x1372,2699:1372,c145_dt_diff_at_e1.PNG)

File: 7404a7681bb820e⋯.png (460.08 KB,2740x1596,685:399,c145_dt_diff_at_e0.PNG)

>>3300

Looked a bit further into (f,1) records, and analyzing the d[t] and a[t] differences.

See pics related for c=145, showing diffs at (e,1), (f,1) and (0,1).

In (f,1), there are more occurrences of the 5 factor in d[t] - d. But unfortunately, that pattern doesn't extend to other test cases. For c=6107, no records appear.

Similarly in (0,1) we get some matches at d[t]-d, but none at a[t].

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4cf7a6 No.3349

File: 9a15f9aebcacadf⋯.png (1.15 MB,1130x711,1130:711,ePos_Shft_Dwn1_Rt2.png)

File: 0ad5845a2081c53⋯.png (1.1 MB,1109x708,1109:708,ePos_Shft_Up1_Rt2.png)

File: 8c97f8fe54981ae⋯.png (929.17 KB,1096x701,1096:701,ePos_Shft_Perspective.png)

File: 4a0d0d19a4d6fd9⋯.png (1 MB,1186x689,1186:689,ePos_eNeg_Folded_e0_noShif….png)

File: cd8b705937b4208⋯.png (1.17 MB,1256x711,1256:711,ePos_eNeg_Folded_e0_Shift_….png)

>>3347

That's cool CA, love your images!

Yes, that's exactly the pattern.

Also trying to look at the shifting / reflecting / twisting perspective.

Attached are the first set, looking at +e. Printed 2 copies and overlayed on light table. Then shifted. The darker cells are the ones where you would be able to jump and land on a cell (valid transform or not).

The perspective view makes the angled lines jump out. The strongest at n=0, e=0, which is probably the Root O D. These make sense with the math as well, including the slope (e can increase by 2 for each increase in one unit).

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4cf7a6 No.3350

File: de6003c567a097c⋯.png (1.03 MB,1219x637,1219:637,eNeg_Shft_Dwn1_Lft2.png)

File: 9ef2998b8b00b8c⋯.png (992.86 KB,1131x720,377:240,eNeg_Folded_along_e_Shift_….png)

File: 5b747c47f260af5⋯.png (1.07 MB,1242x709,1242:709,eNeg_Folded_along_e_Shift_….png)

File: 5b747c47f260af5⋯.png (1.07 MB,1242x709,1242:709,eNeg_Folded_along_e_Shift_….png)

File: 504982cce4773f2⋯.png (1.22 MB,1178x716,589:358,eNeg_VQC_Vortex.png)

>>3349

Ok, to finish off these playful patterns.

Looking at just the Negative e and shifting. These show the strongest lines, with a primary line slope of 2 running away from each perfect square at the n=0 origin. Other lines run different direction, opposite slope, but not 2.

Next reflecting along hortizontal axis (along an n) with the -e space. What is interesting about this, is that each perfect square e column has no gaps, meaning, you could jump from n to -n, back and forth. I think this would mean move along a perfect square column -e toward n=0, but, if you run into a gap, then skip over to the other side (plus n), and carry on toward n=0 until a gap, then jump back, and so on.

Finally a little rotation for fun - the VQC Vortex.

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5167b5 No.3351

Do we have a collection of Chris' crumbs?

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4cf7a6 No.3352

File: ef9ed047e09b501⋯.png (33.58 KB,414x741,138:247,PMA-100657_2_1_pattern.png)

File: d0273e2825f72c5⋯.png (35.42 KB,411x806,411:806,PMA-100657_1_1_pattern.png)

>>3348 Nice!

Interesting, the t diff binary pattern really jumps out visually.

Also reminds me of some patterns from a while back, think it was you?

Just that the a for an n, plus x, plus a for n+1 is the new a (at n+1), the a for n+1 is b for n. This looping pattern that cascades down.

Another pattern is the final digits for a, b, and c. For (2,1), c always ends in a 3, 7 or 1 digit.

For (1,1), it's always a 5 or a 1 for c. Similar patterns in a and b.

Reminds me to looking into modular forms for our a's, b's and c's for patterns and what they say about the rates of change, or about the factors / relationships.

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80a6b3 No.3353

>>3339

Just use the // operator for integer division instead and you won't be limited by then size of floats. Can even get rid ot the explicit int() conversions.

(newX*(newX+2)+E)//2

Alternatively since you're always dividing by two, its much faster to just shift right by one bit than performing an actual division

(newX*(newX+2)+E)>>1

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d7e5a7 No.3355

>>3353

Yeah I changed it to make it better. Now

newX = E%2

if(newX == 1):

dShift = 6

else:

dShift = 4

newD = int((newX*(newX+2)+E)//2)

newA = newD - newX

while(gcd(newD-D,newA) == 1):

newX += 2

newD += dShift

dShift += 4

newA = newD - newX

newA = D - newX

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d7e5a7 No.3356

>>3355

Also you can use any number for the D value. Also the D values are the same as the A values for the (e-1,1) cell.

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4cf7a6 No.3357

File: 11b359261c3e9d3⋯.png (8.8 KB,483x213,161:71,d_to_a_broken_-39_to_-40.png)

>>3356

> Also the D values are the same as the A values for the (e-1,1) cell.

-> Be careful, looks as if that only holds for initial e that are even. The D is same as the (e-1, 1, t+1) A if starting e is odd.

But, in the orig VQC output, this isn't always consistent in the negative e space, there are a few odds that are the same. Might be an artifact of where t=1 started and incorrect grid production (see attached image, e=-39 to e=-40 isn't same pattern as others).

And by extension, the D values are the same as the B values for the (e-1, 1, t-1) cell if e is even, and the same for the (e-1, 1, t) cell if e is odd.

Interestingly, this pattern holds in the negative e space for n=0, if jumping from perfect square to square (-9 to -16, -36 to -49), as shown in first image in previous post here >>3344. Need to validate further, but looks consistent.

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ff4dbe No.3358

>>3351

See >>1721

Hopefully you trust the people here enough to open a pdf. I made it. I couldn't think of a better filetype that could be uploaded to 8ch.

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ab40e5 No.3359

VQC, if you're reading, can I show this to my Number Theory professor? I don't know if I can trust him because he does work a liberal university, but it would be nice to get another set of eyes on it. Also is it dangerous to go public with this?

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ab8fb8 No.3360

>>3359

Hardly. It's just another conspiracy theory

.

.

.

Until it works.

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ab8fb8 No.3364

File: b88b49e07dbd290⋯.jpg (199.63 KB,2184x1456,3:2,piekarz.jpg)

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ab8fb8 No.3365

Discovered something neat.

There's multiple solution records in (e,1), and there's more than one n that solves the number.

145

{1:61:12:11:1:145} (1, 61, 6)

{1:1:32:7:25:41} (1, 1, 4)

{1:5:12:7:5:29} (1, 5, 4)

{1:1:882:41:841:925} (1, 1, 21)

{1:-29:12:41:-29:-5} (1, -29, 21)

123

{2:51:11:10:1:123} (2, 51, 6)

{2:1:41:8:33:51} (2, 1, 5)

{2:11:11:8:3:41} (2, 11, 5)

{2:1:113:14:99:129} (2, 1, 8)

{2:-33:11:52:-41:-3} (2, -33, 27) [not sure why t changes here]

95

{14:39:9:8:1:95} (14, 39, 5)

{14:1:19:4:15:25} (14, 1, 3)

{14:3:9:4:5:19} (14, 3, 3)

{14:1:427:28:399:457} (14, 1, 15)

{14:-21:9:28:-19:-5} (14, -21, 15)

77

{13:31:8:7:1:77} (13, 31, 4)

{13:1:8:1:7:11} (13, 1, 1)

{13:1:8:1:7:11} (13, 1, 1)

{13:1:206:19:187:227} (13, 1, 10)

{13:-17:8:19:-11:-7} (13, -17, 10)

287

{31:128:16:15:1:287} (31, 128, 8)

{31:1:65:9:56:76} (31, 1, 5)

{31:8:16:9:7:41} (31, 8, 5)

{31:1:1697:57:1640:1756} (31, 1, 29)

{31:-40:16:57:-41:-7} (31, -40, 29)

7783

{39:3804:88:87:1:7783} (39, 3804, 44)

{39:1:36469:269:36200:36740} (39, 1, 135)

{39:-200:88:269:-181:-43} (39, -200, 135)

{39:1:1077:45:1032:1124} (39, 1, 23)

{39:24:88:45:43:181} (39, 24, 23)

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1b5a8c No.3366

File: 1ff1c1b4464554a⋯.webm (7.84 MB,1000x424,125:53,Factors.webm)

>>3360

Obviously this is no indication of the speed of the algorithm, (I still can't get it for RSA) but it shows that it definitely works.

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ab8fb8 No.3367

>>3366

That the gcd factor algorithm? Upload the code so I can include it

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c5cd6b No.3368

>>3367

It's built into python. I'm assuming it's using Euclid's algorithm

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ab8fb8 No.3369

>>3368

Yeah, but your algorithm. I converted it to Java but made an error somewhere and it didn't work. So it'd be helpful if I could see the full code.

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c5cd6b No.3370

>>3369

def GCD(a, b):

if b == 0:

return a

else:

return GCD(b, a % b)

I think everything else is on here

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52c67f No.3371

File: c17b37364b9ec2c⋯.jpg (98.18 KB,666x500,333:250,DoingYourPart.jpg)

Wow, Anons! I'm reading and absorbing all your posts. Excellent thoughts. Still can't solve for n, but we keep growing in understanding of the Grid. Also, the group we have here is excellent. Glad to be here, looking forward to contributing more when I have something to share. Deus Vult. Cras Es Noster. Carpe Diem. Let's keep going!!! Everyone here is doing their part. Feels good man!!

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52c67f No.3372

File: e575be45648c094⋯.png (380.09 KB,1024x694,512:347,RememberThe8thOfNovember.png)

Reddit meme, lol! Just noticed. have a large stockpile. Here's a better one.

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4cf7a6 No.3373

>>3364

Thanks Baker, new bread looks superb, looking forward to the first slice.

>>3358

This is the pdf I use first for crumbs, nice compilation, have on phone. Probably everything needed is in there to unlock this with the (n)KEY.

Have been catching up on the crumbs, starting a couple weeks back, still a month behind. I need to dive into p next.

>>3371

>>3372

Hey VA, good to read you! Maybe a nice UK graphic will pull V in here.

>>3347

CA, I recall your other D grid here >>2890 that was interesting.

>>3233

>Regarding interwoven / interleaved patterns, you'll see theres 4 or 5 I think in (0, 8). 2 isn't a magic number, I suspect that you can find infinite interwoven patterns in any (e, n) if you extend the grid into infinity.

>Maybe there is a limit, but I haven't spent any time looking into it…

Hey Isee, seem to recall Chris specifically saying there are a limited number of patterns, and we should enumerate them (how they GROW). Can't find the crumb right now, but think this is critical. I see a 'pattern' as a 1st, 2nd… order rate of growth (derivatives, you know we're going to end up doing some sort of geometric calculus anons!) for each of our variables, and may include interleaved patterns. Believe we need to be able to extract/recognize/model those patterns from the relevant n=1 row elements, and apply the pattern to the relevant base values to get the jump(s)/shift(s) we need. We will benefit from using an appropriate CHOSEN prime number, multiplied by our c, to help/enable the transformation / ID of factors.

>>3159

>>3171

>>3172

Noted your D-sequence is the same I listed earlier here >>3344

Formula is: a(n) = floor((n^2-2*n+3)/2)

in Excel: =FLOOR.MATH(((E10+1)^2-2*(E10+1)+3)/2)

where E is an 'x' value, these increment by one. But as I mention, appears to break down later after the 53rd x. Perhaps the other method would work, or if you could share more details on how you're generating that would be appreciated.

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4cf7a6 No.3374

File: 48f571c2c50c9cc⋯.png (10.73 KB,788x277,788:277,d_c_calculator_1.png)

File: 21269db1c8fbc0f⋯.png (12.4 KB,790x190,79:19,d_c_calculator_2.png)

Last bit for today, is a look at n=0, and entering c-values into excel (doing manually still).

This gives a visual for how the "e space" between D values grows over time (+2 for each incremental D).

First column is the D value, sequence of integers. Second column indicates if D is prime (have a lookup table with first 100K primes that goes up to 1.2M). Then D^2, and then diff between squares of D floor and D ceiling. For each increase in D, +2 is added to the e value range.

So for our 145 example, between d of 12 and 13, the gap is 25 (max e, think one less than that actually, need to ignore perfect squares on either side where e=0), and actual e is 24 to reach 169. The 145 input, gap, and e are in the top row.

Another example shown, c=12,657,734,632, e=90,417. The e range up here is 225,013. Still small compared to RSA, but enough to play once all is figured out.

>>3078

Hey VA, if you want to input some numbers to hit that home run, here they are (from Chris), it would break my excel model though!

public static string Rsa100c = "15226050279225333605356183781326374297180681149613806886579084945801229632589528976540003506920061 39"; public static string Rsa100a = "37975227936943673922808872755445627854565536638199"; public static string Rsa100b = "40094690950920881030683735292761468389214899724061"; public static string Rsa100d = "39020571855401265512289573339484371018905006900194"; public static string Rsa100e = "61218444075812733697456051513875809617598014768503"; public static string Rsa100f = "16822699634989797327123095165092932420211999031886";//2d+1-e public static string Rsa100n = "14387588531011964456730684619177102985211280936"; public static string Rsa100x = "1045343918457591589480700584038743164339470261995"; public static string Rsa100x_plus_n = "1059731506988603553937431268657920267324681542931";

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c38ca6 No.3375

>>3374

>>3373

Mr E. My ExcelFag! Love you man. Those digits will break my Excel model too.

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ab8fb8 No.3376

>>3375

One of the things I tried was factorization of (e, n, t+na) instead of c itself because I thought that the smallest a for the c of t+na would also be a for c, however I discovered that this 145 is special, and that doesn't work for all numbers.

(t+na c for rsa617 has 17 as a, which obviously isn't a factor of rsa617.)

Perhaps there is a hidden pattern there. It is very easy to factorize the c from t+na, even for gigantic numbers, but it doesn't give you the right factorization.

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ab8fb8 No.3377

>>3376

Example:

t+na c for 145 = 145*533

the factorization of 145*533 (77285) = 5*15457

5 is a factor of 145, so we factored 145. But this doesn't work for the other numbers. Obviously c*any number is going to have the factors of c in it, but the smallest a isn't always the right a.

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ab8fb8 No.3378

But at least I know this is the right way to go, because I'm starting to see why knowing the pattern of a[t] and d - d[t] is useful - it gives you a way to go through e,1 faster, or without searching at all

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ab8fb8 No.3379

The bruteforce algorithm is the simplest fastest method of factorization that we've come up with so far. There is always one path to the factors of a semiprime - down.

So all it does is decrement t in (e,1) starting 1*c's t until it reaches the right x. There are only 2 steps to the factors of 145 this way.

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ff4dbe No.3380

>>3370

Are you sure it's a good idea to use recursion? If we're dealing with huge numbers, chances are you'll end up with stack overflow. We already had that problem with another method we tried.

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fbb317 No.3384

>>3380

def GCD(a,b):

while(b!=0):

temp = a

a = b

b = temp%a

return a

Would this work?

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ab8fb8 No.3385

"The solution is a decision tree. The first decision is whether remainder is zero. The second decision is whether the remainder is odd or even. What's the third decision?"

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5167b5 No.3386

>>3385

Is this something VQC has said?

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738c11 No.3387

>>3385

The first decision is hardly a decision. Anyone knows that if e is zero then you have it factored, so why include this. This is included because he wants to make the 2nd decision about division by 2. Remainder is odd or even is also the same as asking what is the remainder upon division by 2. Then I'd say the third step would have to do something with the remainder upon division by 3.

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ff4dbe No.3388

>>3385

When did he say that? Link?

>What's the third decision?

At the top of the decision tree, if e = 0, it's a square, so it's not an RSA number (right?). If e != 0, we need to find n or x, which apparently relies on whether it's odd or even. In the second decision, whether it's even or odd determines what t is, but then to calculate t you need to know x, and if you knew x you'd know a. So do we know any other calculations that require knowing if e is even or odd? Otherwise, should we be using this to find relationships?

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ff4dbe No.3389

Last post so I can sticky the new one already

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