Twin Prime Search is a distributed computing

Distributed computing

Distributed computing is a field of computer science that studies distributed systems. A distributed system consists of multiple autonomous computers that communicate through a computer network. The computers interact with each other in order to achieve a common goal...

 project that looks for large twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

s. It uses the programs LLR (for primality test

Primality test

A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not...

ing) and NewPGen

NewPGen

NewPGen is a program used by researchers looking for large prime numbers. It is a program that is used to rapidly presieve a set of candidate numbers, removing those that are definitely composite numbers...

 (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

PrimeGrid

PrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing platform...

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

Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....

as of August 2009.

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.

External links

• Twin Prime Search home page.
• Twin Prime Search forum.