Deeper understanding of the grid and the non-trivial Lookup (named after the zeros of the Riemann Zeta Function).
By controlling the low prime numbers as a product with, an increasing (non-linear) amount of information is forced upon [e',1]. Each of those factors have to appear early and forever after once they appear in the grid. The sequential probability of consecutive primes being in a random value of [e',1] are low and place huge restrictions on the other primes, including a and including the values of x.
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. BigN' comes into play.