On Maximal Prime Gaps

TL;DR

This paper establishes a new upper bound for prime gaps, demonstrating that the gap between consecutive primes is at most twice the square of the logarithm of the larger prime, with implications for prime distribution.

Contribution

The paper introduces a novel upper bound of 2 log^2 p for prime gaps, improving understanding of prime distribution and interval existence for large numbers.

Findings

Prime gaps are bounded above by 2 log^2 p.

The result implies prime existence in specific intervals for large numbers.

Provides a new perspective on prime distribution bounds.

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 $2\log^2{p_n}$. 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.