Twin Prime Search (TPS) is a volunteer 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. In number theory, it is conjectured that there are infinitely many twin primes, and this is known as the Twin prime conjecture.

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 worked in collaboration with PrimeGrid,[2] which did 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 ).

As of April 2022, the current largest twin prime pair known is 2996863034895 · 21290000 ± 1,[5] with 388,342 decimal digits. It was discovered on September 14, 2016.[6]

The decimal representations of the first two primes listed above 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.
  5. ↑ Caldwell, Chris K. "The Prime Database: 2996863034895*2^1290000-1".
  6. ↑ "World Record Twin Primes Found!".
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