# A Statistical Approach to Prime Gaps and Andrica's Conjecture

## TL;DR

This paper employs statistical methods to analyze prime gaps and provides evidence supporting Andrica's conjecture, including a proven case for at least half of the instances and a derived bound for the conjecture's expression.

## Contribution

It introduces a novel statistical approach to prime gaps and offers new partial proofs and bounds for Andrica's conjecture.

## Key findings

- Andrica's conjecture holds for at least half of the cases.
- A new bound for Andrica's expression is established.
- Statistical analysis supports the conjecture's general validity.

## Abstract

We examine the prime gaps using a statistical approach. It is first shown that the Andrica's conjecture is true for half or more cases. Using the arguments of averages, it is further shown that Andrica's conjecture is true. We further obtain a precise bound for the Andrica's expression.