>>5159

Working on improving the quadratics to help verify (x+n) iteration path. Check this out, found a major (but very basic) improvement for the formula. Staet with the difference of squares equation, and sub in (Tu XPN Est) for the small square. Then begin to solve the equation for n (isolate n). When taking SQRT of c and (Tu XPN Est), we need to include the remainders of both c and (Tu XPN). c = dd + e. For clarity, I'll call remainder of SQRT(Tu XPN) var g.

c = (d+n)^2 - (Tu XPN Est)^2

c + (Tu XPN Est)^2 = (d+n)^2

Floor SQRT(c) + e + Floor SQRT(Tu XPN Est) + g = d + n

dd + e + (Tu XPN Est) + g = d + n

dd + e + (Tu XPN Est) + g - d = n

We're looking for a match where n is a whole integer. Should be easy to spot in a list of calcs.

>>5223

Whoa.

>to understand the Power of him that sits upon the Fire.

We are definitely searching for the underlying numerical order of the universe, which would be related to pi, music, color, sound, DNA, everything, created by the Power of him who sits on the fire.

Your idea about 7 being 111 in binary brought this crumb to mind that I've attached. VQC said that the connection gap between (1,c) and (prime) records in the grid is easier to see in Binary. Have we explored this yet, Anons? Maybe the missing link is easier to see when look at the gap in binary. (e,1) is supposed to be the key to the whole grid?

>>5230

Great work PMA! So it is a recursive adding back in of remainders? I studied your output closely and understand. This example is the prime, but it also works for capstone and starting c as well?

So to clarify, we iterate by n0, but check each iteration against all possible remainders?

I never thought remainders would be so important again! Who would have known, lol :)

>>5231

Read the article, and I think that's what VQC is hinting at! Integers are grouped into families somehow.

>>5232

Seconded. PMA is our MVP for sure!

>>5463

Yup, the most recent use of mod in our quest is solving the odd (x+n) square. We divide the square into 8 Triangles -1. The mod is the remainder left over after dividing into 8 matching triangles. Example:

(x+n)^2= 15^2 = 225

225 - 1 = 224

224 / 8 = 28

224 mod 8 = 0 (bc there is no remainder in this case)

Your cicada friend seems to be hinting that knowing how to properly deal with the remainders is a big key. PMA has done a great job on explaining our current process ==>>>>

>>5257

>the remainder is the mod

>>5260

>>5317. PMA's excellent explanation.

>XPN = 1 + 8T(u) + mod + 8 * (remainder) + mod - (rm 2d(n-1))

>XPN = 1 + 8T(7875) + 4 + 8 * 2440500 + 4 - 1128