Primality proving with Gauss and Jacobi sums

Abstract

This article presents a primality test known as APR (Adleman, Pomerance and Rumely) which was invented in 1980. It was later simplified and improved by Cohen and Lenstra. It can be used to prove primality of numbers with thousands of bits in a reasonable amount of time. The running time of this algorithm for number N is O((ln N)C ln ln ln N}) for some constant C. This is almost polynomial time since for all practical purposes the function ln ln ln N acts like a constant.