Yahya's Cyclic Prime Residue Framework

Abstract

This paper presents an observation regarding the distribution of prime numbers whenmapped onto a repeating seven-letter cyclic labeling system. By labeling integers with aperiodic sequence of seven symbols (A–G), where each symbol corresponds to a residueclass modulo 7, a notable variance in the distribution of prime numbers arises across successive seven-integer blocks. The pattern suggests that primes exhibit non-uniform clusteringacross residue classes in locally bounded ranges, while maintaining long-term equidistribution statistically. This paper outlines the observed pattern, formalizes the structure behindit, provides theoretical context based on modular arithmetic, and introduces the open-sourcecomputational framework accompanying this research.