Twin Prime Search (TPS) is a

volunteer computing Volunteer computing is a type of distributed computing in which people donate their computers' unused resources to a research-oriented project, and sometimes in exchange for credit points. The fundamental idea behind it is that a modern desktop co ...

project that looks for large

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...

s. 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 worked in collaboration with

PrimeGrid PrimeGrid is a volunteer computing project that searches for very large (up to world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing ...

, 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. The

primes A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

are 65516468355 × 2³³³³³³ ± 1, and have 100,355 digits. The smaller of the two primes is also the largest known

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

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 current largest twin prime pair known is 2996863034895 · 2^1290000 ± 1, with 388,342 decimal digits. It was discovered on September 14, 2016. 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 : 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'' × 2^1,000,000 ± 1.

References

External links

* {{Official website, 1=http://primes.utm.edu/bios/page.php?id=949
Twin Prime Search
forum Volunteer computing projects Distributed prime searches

Progress

Current efforts

See also

References

External links