On Maximal Prime Gaps
Number Theory
2026-05-22 v2
Abstract
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 and its consecutive prime number is not larger than . 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.
Cite
@article{arxiv.2605.14871,
title = {On Maximal Prime Gaps},
author = {Cheng-TIng Wang},
journal= {arXiv preprint arXiv:2605.14871},
year = {2026}
}
Comments
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