Twin Prime Search

Twin Prime Search (TPS) is a distributed computing project that looks for large twin primes.[1] 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.

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,[2] 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.[3] The primes are 65516468355 × 2333333 ± 1, and have 100,355 digits.[4] 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.

See also

References
  1. Korevaar, Jacob (2009). "Prime pairs and the zeta function". Journal of Approximation Theory. 158 (1): 69–96. doi:10.1016/j.jat.2008.01.008. ISSN 0021-9045.
  2. Bertil Schmidt (August 21, 2007). "A survey of desktop grid applications for e-science". International Journal of Web and Grid Services. 3 (3): 354–368. doi:10.1504/ijwgs.2007.014957. ISSN 1741-1114. PrimeGrid (2007) is currently running two subprojects: Primegen and Twin Prime Search. Primegen generates a public sequential prime number database. Twin Prime Search searches for large twin primes of the form k·2n + 1 and k·2n – l. ...
  3. PrimeGrid News archive. 2009-08-06. Retrieved 2009-08-22.
  4. "The Prime Database: 65516468355*2^333333-1". Prime Pages. 13 August 2009. Retrieved 2009-08-22.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.