Large gaps between consecutive prime numbers containing square-free numbers and perfect powers of prime numbers

TL;DR

This paper improves upon previous results regarding the distribution of prime numbers, specifically focusing on the occurrence of square-free numbers and perfect powers of primes within prime gaps.

Contribution

It provides a modified and improved proof related to prime avoidance of square-free numbers and perfect prime powers, advancing understanding of prime distribution.

Findings

Enhanced bounds on prime gaps containing square-free numbers

Refined results on prime gaps with perfect powers of primes

Improved theoretical framework for prime avoidance phenomena

Abstract

We prove a modification as well as an improvement of a result of K. Ford, D. R. Heath-Brown and S. Konyagin concerning prime avoidance of square-free numbers and perfect powers of prime numbers.