Twin Prime Search (TPS) is a distributed computing project that looks for large twin primes. It uses the programs LLR (for primality testing) and NewPGen (for sieving). It was founded on April 13, 2006 by Michael Kwok. It is unknown whether there are infinitely many twin primes.
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Progress
TPS found a record twin prime, 2003663613 × 2195000 ± 1, on January 15, 2007, on a computer operated by Eric Vautier. It is 58,711 digits long, which made it the largest known twin prime at the time. The project works in collaboration with PrimeGrid, which does most of the LLR tests.
On August 6, 2009 those same two projects announced that a new record twin prime had been found. The primes are 65516468355 × 2333333 ± 1, and have 100,355 digits. The smaller of the two primes is also the largest known Chen prime as of August 2009.
On December 25, 2011 Timothy D Winslow found the world's largest known twin primes 3756801695685 × 2666669 ± 1 (official announcement: http://www.primegrid.com/download/twin-666669.pdf ).
The decimal representations of the two primes are at http://4unitmaths.com/tp1.pdf and http://4unitmaths.com/tp2.pdf
Current efforts
TPS has three sub-projects as of 2010: A search for k×2390000± 1, a variable twin search to find twins between 144,500 and 150,500 digits, and a search called Operation Megabit Twin for k×21,000,000 ± 1.