Primes between consecutive powers

TL;DR

This paper improves explicit bounds on the existence of primes between consecutive powers, establishing at least one prime between n^{155} and (n+1)^{155} for all n ≥ 1 using advanced explicit estimates.

Contribution

It provides a new explicit interval estimate for primes between consecutive powers, refining previous bounds with a novel version of Goldston's error estimate.

Findings

At least one prime exists between n^{155} and (n+1)^{155} for all n ≥ 1

Introduces a new explicit version of Goldston's 1983 error estimate

Enhances understanding of prime distribution between large powers

Abstract

This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between $n^{155}$ and $(n+1)^{155}$ for all $n\geq 1$. This result is in part obtained with a new explicit version of Goldston's 1983 estimate for the error in the truncated Riemann--von Mangoldt explicit formula.