The Abdeslam Prime Balance Law: A Fundamental Constraint on Prime Gaps at Infinity

Prime numbers appear irregular, yet their gaps follow a hidden pattern. As primes grow larger, the gaps between them widen, but their relative size steadily decreases. The Abdeslam Prime Balance Law states that the ratio of a prime gap to the prime itself approaches zero at infinity. This means that while absolute gaps increase, they become proportionally smaller compared to the primes they separate. This study confirms the law through empirical analysis up to 10 11 10 11 , showing strong agreement with the Prime Number Theorem. The results also align with Cramér’s Conjecture and the Hardy-Littlewood k-tuple model, reinforcing its validity. Beyond number theory, this discovery provides a new way to measure prime distribution, with potential applications in cryptography, AI-driven prime analysis, and the broader study of numerical patterns. This is the first explicit formulation of a deterministic constraint on prime gaps, offering fresh insight into the structure of prime numbers.