To join, head to Great Internet Mersenne Prime Search (GIMPS) website.
Download the software of your platform there.
Create an account with GIMPS.
Then join the SillyDog701 Team
(*) There's an award for people who find the largest prime number. (detail)
If prime number is not your interest, there are many other projects such as BOINC, World Community Grid... etc. (I am sure Richard can tell you more about those.)
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