Number Theory

    

Theory of Quadratic Triadic Relations for Prime Numbers

Authors: Youssouf Ouédraogo

This paper proposes a new structural approach to the study of consecutive prime numbers based on a quadratic relation linking three successive primes. A stability ratio is introduced and shown to converge asymptotically to unity using explicit bounds for the k-th prime number. This convergence induces a constraint on the local variation of prime gaps, leading to an asymptotic smoothness law for their relative fluctuations. The analysis is fully deterministic and avoids heuristic arguments based on average asymptotic. Numerical validations using verified large prime datasets confirm the theoretical predictions and illustrate the progressive regularization of local gap variations as the prime index increases.

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[v1] 2026-01-12 20:50:18

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