Primes and Applications

With John Dusel and Jason Erbele

For millennia the patterns formed by numbers have fascinated people. Prime numbers have played an important role in that history, ranging from cool curiosities to public key encryption. This project will provide an overview of some of the important tools and results in number theory, with a focus on the prime connection.

The mathematical core of this project includes a study of prime integers, congruences, the prime number theorem, and the notion of primeness in other mathematical systems such as polynomials and the Gaussian integers. On the practical side: With the help of software packages like Mathematica we will study distribution of primes, factorization methods, linear diophantine equations, and the RSA cryptosystem. This project is open to motivated sophomores, juniors and seniors.