For anyone who doesn't already know of it, the GIMPS project links up computers worldwide to search for the next Mersenne Prime number (of the form 2^n - 1) --- anyone with a personal computer can participate, and even win cash rewards (and all the work is done on your computer in the background, while you wile away the hours surfing the Web and eating pizza!).
If interested check it out here:
Some history/background on Mersenne primes:
or the Wikipedia account:
...and more updated info on primes here:
Finally, the largest current Mersenne prime (at the moment): 243112609 -1