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arXiv · 2605.14871

On Maximal Prime Gaps

Cheng-TIng Wang
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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 $p_n$ and its consecutive prime number is not larger than $\frac{13}{3}\log^2{p_n}$. 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.

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Cheng-TIng Wang. 2026-05-14. On Maximal Prime Gaps. https://arxiv.org/abs/2605.14871

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