The Great International Mersenne Prime Search (GIMPS) wants you to help in their search for Mersenne primes. These are prime numbers of the form (where p is itself a prime) and they can be found by anyone! The largest was found last November by a student. It has 6,320,430 decimal digits.
You could win fame and fortune so go along to http://www.mersenne.org/prime.htm where it says:
“You could discover one of the most coveted finds in all of Mathematics – a new Mersenne prime number. We’ve found six already. Join in on this fun, yet serious research project. All you need is a personal computer, patience, and a lot of luck.
In addition to the joy of making a mathematical discovery, you might win some cash. The Electronic Frontier Foundation is offering a $100,000 award to the first person or group to discover a ten million digit prime number! See how GIMPS will distribute this award if we are lucky enough to find a ten million digit prime.“