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. Each of these discoveries are currently the largest and second largest known pairs in their respective categories.

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