| _version_ | 1866902209248100352 |
|---|---|
| author | Ouédraogo, Youssouf |
| author_facet | Ouédraogo, Youssouf |
| contents | <p><span lang="EN-US">This work introduces a new structural approach to the study of prime numbers based on local quadratic relations between three consecutive primes. Instead of focusing solely on global averages or probabilistic distributions, the article investigates the internal stability of prime triplets and the constraints imposed by their mutual interaction.</span></p> <p><span lang="EN-US">A stability ratio is defined to measure the deviation from a quadratic equilibrium between consecutive primes. Using explicit analytic bounds for prime numbers, the study proves that this ratio converges asymptotically to unity and that the convergence follows a quadratic decay rate. This result leads to the formulation of a quadratic equilibrium law governing the asymptotic behavior of prime triplets.</span></p> <p><span lang="EN-US">An exact algebraic identity is derived linking the stability ratio to the local variation of prime gaps. From this identity, a new asymptotic smoothness law is established, showing that although prime gaps remain irregular in absolute terms, their relative variation becomes negligible as primes grow larger. This reveals a second-order regularity in the prime sequence that is not captured by classical average results.</span></p> <p><span lang="EN-US">The theoretical analysis is supported by extensive numerical verification, including tests on large prime triplets and data extracted from known prime constellations. These validations confirm the robustness of both the quadratic equilibrium law and the asymptotic smoothness law in high numerical regimes.</span></p> <p><span lang="EN-US">The results provide a new structural constraint on the local dynamics of prime numbers, offering a complementary perspective to existing analytic and probabilistic theories. This work aims to contribute to the broader understanding of prime number behavior by introducing a deterministic framework that captures both local stability and asymptotic regularity.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18089423 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Theory of Quadratic Triadic Relations for Prime Numbers Ouédraogo, Youssouf Prime numbers, quadratic discriminant, Bertrand's theorem, triadic relations, prime gaps, consecutive primes, asymptotic analysis, local bounds of prime numbers <p><span lang="EN-US">This work introduces a new structural approach to the study of prime numbers based on local quadratic relations between three consecutive primes. Instead of focusing solely on global averages or probabilistic distributions, the article investigates the internal stability of prime triplets and the constraints imposed by their mutual interaction.</span></p> <p><span lang="EN-US">A stability ratio is defined to measure the deviation from a quadratic equilibrium between consecutive primes. Using explicit analytic bounds for prime numbers, the study proves that this ratio converges asymptotically to unity and that the convergence follows a quadratic decay rate. This result leads to the formulation of a quadratic equilibrium law governing the asymptotic behavior of prime triplets.</span></p> <p><span lang="EN-US">An exact algebraic identity is derived linking the stability ratio to the local variation of prime gaps. From this identity, a new asymptotic smoothness law is established, showing that although prime gaps remain irregular in absolute terms, their relative variation becomes negligible as primes grow larger. This reveals a second-order regularity in the prime sequence that is not captured by classical average results.</span></p> <p><span lang="EN-US">The theoretical analysis is supported by extensive numerical verification, including tests on large prime triplets and data extracted from known prime constellations. These validations confirm the robustness of both the quadratic equilibrium law and the asymptotic smoothness law in high numerical regimes.</span></p> <p><span lang="EN-US">The results provide a new structural constraint on the local dynamics of prime numbers, offering a complementary perspective to existing analytic and probabilistic theories. This work aims to contribute to the broader understanding of prime number behavior by introducing a deterministic framework that captures both local stability and asymptotic regularity.</span></p> |
| title | Theory of Quadratic Triadic Relations for Prime Numbers |
| topic | Prime numbers, quadratic discriminant, Bertrand's theorem, triadic relations, prime gaps, consecutive primes, asymptotic analysis, local bounds of prime numbers |
| url | https://doi.org/10.5281/zenodo.18089423 |