This paper presents empirical evidence demonstrating that the local distribution of prime numbers is strictly governed by localized deterministic constraints, challenging purely probabilistic macro-level frameworks like Cramér's random model. Through a computational analysis of twin (gap 2), cousin (gap 4), and sexy (gap 6) prime pairs up to 2 million, the study introduces the Information Potential heuristic I=2p+(g−1). The findings reveal a staggering near-universal adherence to a harmonic lattice of step 6: approximately 99% of twin and cousin primes—and 49% of sexy primes, with the remaining half structurally excluded by modulo 3 constraints—land within a ±48 offset of another prime. This research highlights the intense, localized modular architecture that operates beneath the pseudo-random macro-distribution of primes.
Massimiliano Concas (Tue,) studied this question.