English

The Differences Between Consecutive Primes. V

Number Theory 2019-06-25 v1

Abstract

We show that pnxpn+1pnpn(pn+1pn)εx3/5+ε\sum_{\substack{p_n\le x\\ p_{n+1}-p_n\ge\sqrt{p_n}}}(p_{n+1}-p_n)\ll_{\varepsilon} x^{3/5+\varepsilon} for any fixed ε>0\varepsilon>0. This improves a result of Matom\"{a}ki, in which the exponent was 2/32/3.

Keywords

Cite

@article{arxiv.1906.09555,
  title  = {The Differences Between Consecutive Primes. V},
  author = {D. R. Heath-Brown},
  journal= {arXiv preprint arXiv:1906.09555},
  year   = {2019}
}
R2 v1 2026-06-23T10:00:59.352Z