| _version_ | 1866902057706848256 |
|---|---|
| author | Okolo, Hanyelichukwu Paul |
| author_facet | Okolo, Hanyelichukwu Paul |
| contents | <div> <div> <div> <p>This paper presents a complete and unconditional proof of a strong form of the Elliott-Halberstam (EH) conjecture and, as a direct consequence, the Twin Prime Conjecture. The proof demonstrates that a failure of the EH conjecture would imply the existence of a widespread ”conspiracy” among prime numbers. We then prove that such a conspiracy would, in turn, necessitate a structure of zeros for Dirichlet L-functions that is rigorously excluded by the established, rock-solid theorems of Page and Siegel. By formalizing this contradiction, we prove that primes are sufficiently well-distributed in arithmetic progressions for modern sieve methods to apply, which unconditionally proves the infinitude of twin primes.</p> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15665182 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An Unconditional Proof of the Elliott-Halberstam and Twin Prime Conjectures. Okolo, Hanyelichukwu Paul Number theory Prime numbers Prime numbers Twin Prime Conjecture Riemann Hypothesis Riemann Zeta Function Analytic Geometry Analytic Number Theory Mathematical Proof <div> <div> <div> <p>This paper presents a complete and unconditional proof of a strong form of the Elliott-Halberstam (EH) conjecture and, as a direct consequence, the Twin Prime Conjecture. The proof demonstrates that a failure of the EH conjecture would imply the existence of a widespread ”conspiracy” among prime numbers. We then prove that such a conspiracy would, in turn, necessitate a structure of zeros for Dirichlet L-functions that is rigorously excluded by the established, rock-solid theorems of Page and Siegel. By formalizing this contradiction, we prove that primes are sufficiently well-distributed in arithmetic progressions for modern sieve methods to apply, which unconditionally proves the infinitude of twin primes.</p> </div> </div> </div> |
| title | An Unconditional Proof of the Elliott-Halberstam and Twin Prime Conjectures. |
| topic | Number theory Prime numbers Prime numbers Twin Prime Conjecture Riemann Hypothesis Riemann Zeta Function Analytic Geometry Analytic Number Theory Mathematical Proof |
| url | https://doi.org/10.5281/zenodo.15665182 |