I've been thinking about the "lookup x", if anyone remembers that. At the time nobody seemed to have any idea what it meant to have an x value in (e,1) or (f,1) that would lead to the solution that wouldn't just be the x we were already looking for (thereby rendering it meaningless to apply it to (e,1) and (f,1) since we'd already have an unknown that would give us the solution). It's a lookup x that's meant to either give us na or n-1. I'm thinking maybe this refers to the binary chunk thing. It's the only thing that's come up since he introduced the concept of a lookup x that seems to give it any meaning (a lookup x that gives us the element where na or n-1 is a chunk at the end of a[t] in binary). I've run some tests looking for na or n-1 in binary at the end of a[t] in elements other than the six we were using before and I haven't run into any that it doesn't work for yet, but the ones it works for where it isn't one of the six known elements, I haven't seen anything yet that would give a path to this x value. Here are two examples (I had to use numbers in the thousands or these tests would have taken hours (RSA_100 would have taken at most ten octovigintillion years with this algorithm, so maybe not that one) - also there are other examples that found n-1 but these both happen to be na):
(123,222,521) = {123:222:3482:1041:2441:4967}, f=-6842, c=12124447, u=631, i=3704, j=1263
The x values for the six known elements are (e,1) 12120965, 3481, 12127929 and (f,1) 12107038, 3480, 12114003
Found na at (f,1) x=11659973 === (146580344905683,1,5823023) = {146580344905683:1:141105366169899:11646045:141105354523854:141105377815946}, f=-135630387434116, c=19910724361941423765278575884, u=5823022, i=141105366169900, j=11646046
12107038 - 11659973 = 447065, so the solution element is 223533 elements below the (f,1) a[t]=c*(BigN-1) element
(3012,276,472) = {3012:276:2555:942:1613:4049}, f=-2099, c=6531037, u=608, i=2831, j=1218
The x values for the six known elements are (e,1) 6528482, 2554, 6533592 and (f,1) 6528481, 2555, 6533592
Found na at (e,1) x=6292398 === (3012,1,3146200) = {3012:1:19797142589106:6292398:19797136296708:19797148881506}, f=-39594285175201, c=39192685469339Post too long. Click here to view the full text.