One conjecture to rule them all: Bateman-Horn

Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, Stephan Ramon Garcia

Published 2018-07-24Version 1

The Bateman-Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green-Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau's conjecture. We discuss the Bateman-Horn conjecture, its applications, and its origins. No knowledge beyond elementary undergraduate number theory is assumed.