Twin Prime Search

This article will address the topic of Twin Prime Search, which has gained relevance in recent years due to its impact on various areas of society. Since its emergence, Twin Prime Search has sparked the interest of experts and ordinary people alike, generating debates and reflections around its influence on daily life. Through this analysis, we seek to offer a broad and complete vision of Twin Prime Search, examining its multiple facets and exploring the implications it has in the current context. By reviewing various points of view and presenting relevant information, we will seek to provide the reader with a comprehensive understanding of Twin Prime Search and its importance today.

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]

On December 25, 2011, Timothy D Winslow found the world's largest known twin primes 3756801695685 × 2666669 ± 1. [5]

As of February 2024, the current largest twin prime pair known is 2996863034895 · 21290000 ± 1,[6] with 388,342 decimal digits. It was discovered on September 14, 2016.[7]

Current efforts

TPS has two subprojects as of 2024. These subprojects include a variable twin search to find twins between 144,500 and 150,500 digits, and a search called the "Operation Megabit Twin" for primes larger than k × 21,000,000 ± 1.[8]

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. ^ "PrimeGridʼs Sophie Germain Prime Search" (PDF). Archived from the original (PDF) on 2023-11-27.
  6. ^ Caldwell, Chris K. "The Prime Database: 2996863034895*2^1290000-1".
  7. ^ "World Record Twin Primes Found!".
  8. ^ "Twin Prime Search". The PrimePages.