The Great Internet Mersenne Prime Search is a 'distributed computing' project whose aim is to find - what else? - Mersenne primes. Rather than go into the subject in any detail I will give you a link to the GIMPS home page where all will be explained..!
I have been participating in the GIMPS project for more than fifteen years - so far I have not made it into the math history books - but there's always hope...
SETI@home is another interesting 'distributed computing' project in which participants analyse data acquired by the Arecibo radio telescope in the Search for Extra-Terrestrial Intelligence. If you get a 'hit' on this one your name really will be in the record books...!
Details and to dowload software - click here