Twin Prime Search
{{Short description|Volunteer computing project seeking large twin primes}}
{{Update|part=Current efforts|date=April 2023}}
Twin Prime Search (TPS) is a volunteer computing project that looks for large twin primes.{{Cite journal|last=Korevaar|first=Jacob|year=2009|title=Prime pairs and the zeta function|journal=Journal of Approximation Theory|volume=158|issue=1|pages=69–96|issn=0021-9045|doi=10.1016/j.jat.2008.01.008|doi-access=free}} 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,{{cite journal|date=August 21, 2007|author=Bertil Schmidt|title=A survey of desktop grid applications for e-science|journal=International Journal of Web and Grid Services|volume=3|issue=3|pages=354–368|issn=1741-1114|quote=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. ...|doi=10.1504/ijwgs.2007.014957}} 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.[http://www.primegrid.com/all_news.php#188 PrimeGrid News archive]. 2009-08-06. Retrieved 2009-08-22. The primes are 65516468355 × 2333333 ± 1, and have 100,355 digits.{{cite web | url = http://primes.utm.edu/primes/page.php?id=89650 | title = The Prime Database: 65516468355*2^333333-1 | work = Prime Pages | date = 13 August 2009 | accessdate = 2009-08-22}}
On December 25, 2011, Timothy D Winslow found the world's largest known twin primes 3756801695685 × 2666669 ± 1. {{cite web|url=http://www.primegrid.com/download/twin-666669.pdf|title=PrimeGridʼs Sophie Germain Prime Search|archive-url=https://web.archive.org/web/20231127211105/http://www.primegrid.com/download/twin-666669.pdf |archive-date=2023-11-27 }}
{{As of|2024|2}}, the current largest twin prime pair known is 2996863034895 · 21290000 ± 1,{{cite web|url=http://primes.utm.edu/primes/page.php?id=122213|title=The Prime Database: 2996863034895*2^1290000-1|first=Chris K.|last=Caldwell}} with 388,342 decimal digits. It was discovered on September 14, 2016.{{cite web|url=http://www.primegrid.com/forum_thread.php?id=7021|title=World Record Twin Primes Found!}}
Current efforts
TPS has two subprojects {{As of|2024|lc=on}}. 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.{{cite web |title=Twin Prime Search |url=https://t5k.org/bios/page.php?id=949 |website=The PrimePages}}
See also
References
{{Reflist|30em}}
External links
- {{Official website|1=http://primes.utm.edu/bios/page.php?id=949}}
- [http://mersenneforum.org/forumdisplay.php?f=65 Twin Prime Search] forum
- [https://t5k.org/top20/page.php?id=1, Top 20 Twin Primes]