Riesel Sieve is a distributed effort to prove the Riesel problem (which states that k=509203 is the smallest possible Riesel number). To do that, they have to find primes for all the remaining k values to prove that they are not Riesel numbers.
How to participate
As of 2005-11-22, 74 k values are left as possible candidates, which need to be eliminated. All 74 are being sieved by Riesel Sieve, but only 69 of them are being LLR tested by Riesel Sieve. The remaining 5 k values are being tested by individuals independent of the Riesel Sieve project. Those values are left over from the time before Riesel Sieve started, when all testing was done independently. As values have been released from testing by individuals, the Riesel Sieve project has taken over testing them.
The sieve (n<50M) reached the optimal sieve zone and it's now suspended.