A Generalized Elliott-Halberstam Conjecture Implying the Twin Prime Hypothesis
Number Theory
2025-11-20 v1
Abstract
We propose a generalization of the Elliott-Halberstam conjecture concerning the distribution of prime pairs in arithmetic progressions. This conjecture, which we call the Generalized Elliott-Halberstam Conjecture for Shifted Convolutions (GEH-2), provides a level of distribution for correlations of the von Mangoldt function. We show that GEH-2 implies the twin prime conjecture, describe heuristic and analytic motivation, and discuss implications for prime gaps and -tuple patterns.
Keywords
Cite
@article{arxiv.2511.14810,
title = {A Generalized Elliott-Halberstam Conjecture Implying the Twin Prime Hypothesis},
author = {Trey Smith},
journal= {arXiv preprint arXiv:2511.14810},
year = {2025}
}
Comments
5 pages, 10 references