A Note on the Andrica Conjecture

TL;DR

This paper heuristically derives an approximate formula for the difference between square roots of consecutive primes and validates it against known maximal prime gaps, providing insights into prime distribution.

Contribution

It introduces a heuristic formula for prime gap differences based on square roots and confirms its accuracy with empirical data.

Findings

Heuristic formula matches observed prime gap data.

Provides a new perspective on prime distribution patterns.

Supports conjectures related to prime gaps.

Abstract

We derive heuristically the approximate formula for the difference $\sqrt{p_{n+1}} - \sqrt{p_n}$, where $p_n$ is the n-th prime. We find perfect agreement between this formula and the available data from the list of maximal gaps between consecutive primes.