中文

On Maximal Prime Gaps

数论 2026-05-22 v2

摘要

In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number pnp_n and its consecutive prime number is not larger than 2log2pn2\log^2{p_n}. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence.

关键词

引用

@article{arxiv.2605.14871,
  title  = {On Maximal Prime Gaps},
  author = {Cheng-TIng Wang},
  journal= {arXiv preprint arXiv:2605.14871},
  year   = {2026}
}

备注

A problem with the original proof in Lemma 2.3 was identified, therefore, I came up with a revised form as an attempt to fix and as a result, the constant part has become different