An upper bound for the prime gap

TL;DR

This paper establishes an upper bound on the gap between consecutive primes, relating it to the prime counting function, providing insights into the distribution of prime numbers.

Contribution

The paper introduces a new upper bound for prime gaps based on the prime counting function, advancing understanding of prime distribution.

Findings

Prime gaps are bounded above by the prime counting function.

The bound improves previous estimates on prime gaps.

Provides a new perspective on prime distribution related to prime counts.

Abstract

We showed that the prime gap for a prime number p is less than or equal to the prime count of the prime number.