Primality Testing for Beginners

In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works.