Primality testing and finding large prime numbers has significant applications to cryptography. In this talk I will discuss a deterministic, polynomial time algorithm for determining if an integer is prime developed by Agrawal, Kayal, and Saxena. Here polynomial time means that there exists constants c,d such that the number of operations to determine if the given integer is prime is less than c log^d(n) where n is the number we are testing for primality.