English

Large prime gaps and progressions with few primes

Number Theory 2022-07-05 v4

Abstract

We show that the existence of arithmetic progressions with few primes, with a quantitative bound on "few", implies the existence of larger gaps between primes less than x than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet L-functions.

Keywords

Cite

@article{arxiv.1907.11994,
  title  = {Large prime gaps and progressions with few primes},
  author = {Kevin Ford},
  journal= {arXiv preprint arXiv:1907.11994},
  year   = {2022}
}

Comments

re-organized the description of the corollaries; typos corrected

R2 v1 2026-06-23T10:32:52.349Z