Prime Numbers in Public Key Cryptography

The subject of prime numbers has fascinated mathematicians for centuries. Some of the methods for finding prime numbers date to antiquity. The properties of primes have been investigated for thousands of years. The advent of digital computers and public-key cryptography has brought the subject of prime numbers into the mainstream and focused renewed attention on it. Prime numbers are interesting entities (you may not believe that now but I'm confident that you will when you have finished reading this paper) that are extremely important in many branches of mathematics. They are also essential to a number of real world algorithms including most of the algorithms used in public key (asymmetric) cryptography. This paper explores some of the basic properties of prime numbers and several theorems associated with them. It also presents moderate detail on two of the most common asymmetric algorithms and the manner in which they employ prime numbers.