The low primes act to filter out the numbers that a cannot be based on what we know in [e,1] and, importantly in [-f,1]. Because one is odd, and one is even, the overlap and distribution of odd numbers in one of these columns and e' is such that a lookup becomes possible.
>So the next thing to look into could maybe be a comparison between the prime factors of each a'[t] value in both (e',1) and (f',1), using consecutive primes for q.
Cool! I'll have time to put in some work on this after my workday is finished. Thanks Senpai for verifying that we're on the right track!