A heuristic study of prime number distribution

TL;DR

This paper heuristically investigates prime number distribution in short intervals, modeling their occurrence as a counting experiment, and provides experimental validation and extension of the Montgomery and Soundararajan conjecture.

Contribution

It introduces a heuristic model for prime distribution in short intervals and extends a notable conjecture with experimental validation.

Findings

Validated the Montgomery and Soundararajan conjecture experimentally

Extended the conjecture to new cases

Provided a heuristic framework for prime distribution analysis

Abstract

This work consists of a heuristic study on the distribution of prime numbers in short intervals. We have modelled the occurrence of prime numbers such intervals as a counting experiment. As a result, we have provided an experimental validation and an extension of the Montgomery and Soundararajan conjecture. This is a reduced version of my bachelor`s thesis presented at the University of Valencia.