Comparing and Reviewing Modern Primality Tests

Abstract

Primality tests refer to algorithms that determine whether a number is prime or composite. These tests are essential to modern encryption algorithms, including the widely used RSA public key encryption algorithm. However, with so many different primality tests out there, choosing the correct one for a given application can be challenging. This paper provides an overview of modern primality tests, detailing the differences between different types of tests and when one test may be preferable to another. Furthermore, implementations of popular primality tests are written and compared to one another graphically to better understand their differing performances. Lastly, we look at next steps for the field of primality tests due to the rise of quantum computing, which could serve as a means of creating even better primality tests.