PrimeGrid Sophie Germain Search

The Sophie Germain Search is a PrimeGrid sub-project searching for Sophie Germain and Twin prime pairs. It was launched in 2009 as a successor to the Twin Prime Search sub-project.

Search range

The current iteration of the project is searching for prime numbers of the form k×2^1290000-1, for k ≤ 10 trillion. Sophie Germain pairs take the form k×2^1290001-1, and Twin pairs take the form k×2^1290000+1.

As of June 2020, the search is currently at k = 5.4 trillion. Live status

The first version of the project searched for prime numbers k×2ⁿ-1 for 666,666 ≤ n ≤ 666,691 with varying ranges of k values up to 38.5 trillion.

Found primes

As of June 2020 the project has found over 8200 primes, with 2 Sophie Germain pairs and 2 Twin pairs.

Sophie Germain pairs

1. 2618163402417•2^1290000-1 and 2618163402417•2^1290001-1 on 2016-02-29, official announcement
2. 18543637900515•2⁶⁶⁶⁶⁶⁷-1 and 18543637900515•2⁶⁶⁶⁶⁶⁸-1 on 2012-04-09, official announcement

Twin pairs

1. 2996863034895•2^1290000-1 and 2996863034895•2^1290000+1 on 2016-09-14, official announcement
2. 3756801695685•2⁶⁶⁶⁶⁶⁹-1 and 3756801695685•2⁶⁶⁶⁶⁶⁹+1 on 2011-12-25, official announcement

See also

• Sophie Germain prime
• Twin prime
• PrimeGrid

External links

• Sophie Germain Prime Search forum introduction thread
• Full list of primes found by project