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I think I did it. I did the thing I set out to do.
let p = a semiprime of simple factors ab.
let f equal the product of b and i=2...a inclusive, where i is all natural numbers from 2 to a.
let s equal some set of prime factors that are b-smooth up to and including some factor n, with no gaps in the set.
m is a the largest primorial such that f%m == 0, where
the factors of s form the base of a series of powers as part of a product x
1. where (x*p) = f
2. and (x*p)%f == a
if statement 2 is untrue, there still exists an algorithm that
3. trivially derives the exponents of s for f, where the sum of those exponents are less than a.
4. trivially generates f from p without knowing a and b.
For those who have followed what I've been trying to do for so long, and understand the math,
then you know this appears to be it.
I'm just writing and finishing the scripts for it now.
Thank god. It's just in time. Maybe we can prevent the nuclear apocalypse with the crash this will cause if it works.