On an upper bound for the prime gap

TL;DR

This paper explores bounds on the differences between primes, focusing on logarithmic and square-root estimates for prime gaps, contributing to understanding the limitations of prime gap sizes.

Contribution

It introduces new bounds for prime gaps based on logarithmic and square-root functions, advancing theoretical understanding of prime distribution.

Findings

Derived upper bounds for prime gaps using logarithmic functions

Established square-root type bounds for prime differences

Provided insights into the limitations of prime gap sizes

Abstract

We investigate logarithmic and square-root types of bounds for the general difference of two primes, $P_{k+q}-P_k$, $k, q\in\mathbb{N}$.