You can obtain a copy of Mathematica for your personal computer through this site. You are required to use Mathematica (or a similar computer algebra program, such as MatLab) for MA 341. There is documentation for using Mathematica in the program you receive, and this page also has a link to additional documentation on the web.

You can participate in the search for Mersenne primes and the largest known prime by going to this website. There is a cash prize of $150,000 to the first person that discovers a prime with 100 million digits. The current largest known prime has just over 12 million digits. There are smaller cash prizes for the discovery of new Mersenne primes. Anyone can enter this contest, no math knowledge is necessary.

Fermat numbers are F_n = 2^{2^n} + 1 . Fermat conjectured they were always prime, however the largest known Fermat prime is F_4 = 65537. It is still unknown whether or not there are any larger Fermat primes. When F_n is not prime there is interest in finding the prime factorizations. This page gives what is known about the prime factorizations of Fermat numbers.

On this site you can search for interesting sequences of integers either by name, (i.e. Fermat Primes) or by entering numbers in a sequence (i.e. 3, 5, 17, 257, 65537 , which is the list of known Fermat primes). Of course you could also play with this by entering numbers in any sequence you think might be interesting. Numberous references are given for sequences.

This is a very interesting and quite well known article describing all of the known attacks on the RSA Cryptography System. As the article says:

"These days RSA is deployed in many commercial systems. It is used by Web servers and browsers to secure Web traffic, it is used to ensure privacy and authenticity of e-mail, it is used to secure remote login sessions, and it is at the heart of electronic credit card payment systems."

"Two decades of research into inverting the RSA function produced some insightful attacks, but no devastating attack has ever been found. The attacks discovered so far mainly illustrate the pitfalls to be avoided when implementing RSA. At the moment it appears that proper implementation can be trusted to provide security in the digital world."

This site tells gives an overview of the different ways to find prime numbers, and how to prove numbers are "probably prime" or actually prime. There are references to the most recent results.