Part 7/9:
As we progress to wider scales, we find that calculations reveal that advancing by 710 points correlates closely with a significant number of rotations near 113 full turns, even more accurately yielding the approximation 355/113 for π. This instance of exceptional rational approximation emphasizes the ordered nature of primes distilled through residue classes mod 710.
With this revelation, distributions form nearly straight lines across the prime number spectrum. Insights into which residue classes remain while filtering for primes lead to an understanding of how they correlate to overall distributions. This analysis builds upon the foundations of deep number theory explorations, such as looking at how primes are partitioned by last digits under different base systems.