About de Polignac's conjecture

TL;DR

This paper proposes a new method to bound gaps between primes using series divergence and discusses implications for Polignac's conjecture, contributing to understanding prime distribution and conjecture validation.

Contribution

Introduces a novel approach leveraging series divergence and logarithmic integrals to analyze prime gaps and Polignac's conjecture.

Findings

Bounded prime gaps derived from series divergence

Implications for Polignac's conjecture discussed

Method offers new insights into prime distribution

Abstract

In this note we present a method to bound gaps between primes via the divergence of the series of reciprocals of the prime numbers, a consequence of a version of the Bertrand's test for convergence of series of positive numbers and a suitable series of positive terms related to the logarithmic integral function. Using this proposed method we discuss the Polignac's conjecture and present some consequences.