This result links to the patterns show in [5], an algorithm to find primes from a pixel map. The number of divisors for a number on the map is the number of lines intersected traversing across it. This means the function \(\Delta\theta(1)_N\) is the sum across thhe diagonals of the map, compressing the algorithm from 2 dimensions to 1.
Because of this, it appears much quicker to generate primes from the \(\Delta\theta(1)_N\) terms in fixed memory. Primes up to around \(50,000\) were generated.