An invitation to additive prime number theory

TL;DR

This survey introduces additive prime number theory to newcomers, covering key problems, historical context, fundamental methods, and current research directions in the field.

Contribution

It provides an accessible overview of additive prime number theory, highlighting main problems, techniques, and recent developments for beginners.

Findings

Overview of main problems in additive prime number theory

Summary of historical development and key methods

Outline of current research directions

Abstract

The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.