English

Recent results on large gaps between primes

Number Theory 2024-09-02 v2

Abstract

One of the themes of this paper is recent results on large gaps between primes. The first of these results has been achieved in the paper [12] by Ford, Green, Konyagin and Tao. It was later improved in the joint paper [13] of these four authors with Maynard. One of the main ingredients of these results are old methods due to Erd\H{o}s and Rankin. Other ingredients are important breakthrough results due to Goldston, Pintz and Yildirim [15, 16, 17], and their extension by Maynard on small gaps between primes. All these previous results are discussed shortly. The results on the appearance of kk-th powers of primes contained in those large gaps, obtained by the author in joint work with Maier [23, 24, 25] are based on a combination of the results just described with the matrix method of Maier.

Keywords

Cite

@article{arxiv.2402.07176,
  title  = {Recent results on large gaps between primes},
  author = {Michael Th. Rassias},
  journal= {arXiv preprint arXiv:2402.07176},
  year   = {2024}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1412.5029, arXiv:1511.04468 by other authors

R2 v1 2026-06-28T14:45:18.072Z