Prime Clustering and Prime Gaps via the Pathak Continuum Compression Hypothesis (PCCH)

Abstract

Prime numbers have fascinated mathematicians due to their seemingly random distribution and mysterious clustering behavior. We propose a new approach based on the Pathak Continuum Compression Hypothesis (PCCH), which views the number line as a continuum affected by arithmetic interaction patterns among numbers. Instead of a generative or causal model of primes, PCCH provides a descriptive and structural reframing of prime number phenomena that captures regularities in prime number clustering and prime number gaps via interaction-weighted compression effects.