Sierpinski/Riesel Base 5
Sierpinski/Riesel Base 5 tries to prove that k=159986 is the smallest possible base 5 Sierpinski number and that k=346802 is the smallest possible base 5 Riesel number. To prove this, one must find primes for all k below the smallest known number.
How to participate
Participants in either of the projects reserve a k in the forum, then use NewPGen to sieve and then LLR to PRP test (for primality). After that, users unreserve their k again if no primes are found. Instructions to the project can be found at OmbooHankvalds guidepages.
As of this moment (2006-10-18), there are 80 Sierpinski and 206 Riesel base 5 candidate k left, which need primes.