Bounded gaps between primes

TL;DR

This paper discusses Zhang's groundbreaking work on bounded gaps between primes and subsequent developments, providing accessible notes aimed at a general mathematical audience, highlighting key ideas and progress in the field.

Contribution

It offers an accessible, colloquium-style overview of Zhang's work and subsequent advances on bounded prime gaps, tailored for a broad mathematical audience.

Findings

Proof of existence of bounded gaps between primes

Development of new techniques in analytic number theory

Progress towards bounded prime gaps conjecture

Abstract

These are notes on Zhang's work and subsequent developments produced in preparation for 5 hours of talks for a general mathematical audience given in Cambridge, Edinburgh and Auckland over the last year. Being for colloquium-style talks, these notes are at a much lower level than other accounts in the literature. In places they are deliberately quite nonrigorous. Whether anyone will find them helpful is unclear but some care was taken on their preparation and there is, I hope, little harm in making them available here.