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PrimeGrid Sophie Germain Search

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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. The project will be suspended on or around 15 December 2023.[1]

Search range

The current iteration of the project is searching for prime numbers of the form k•21290000-1, for k ≤ 1013.

PrimeGrid Forum thread is not current, still data for n=666666 given (k ≤ 41 • 1012).

Sophie Germain pairs take the form k•21290001-1 or k•21289999-1, and Twin pairs take the form k•21290000+1.[2]

As of July 2023, the search is currently at k ≥ 8.3 • 1012. (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 • 1012.

Found primes

As of July 2023 the project has found over 10800 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•21290000-1 and 2618163402417•21290001-1 on 2016-02-29 (official announcement)
  2. 18543637900515•2666667-1 and 18543637900515•2666668-1 on 2012-04-09 (official announcement)

Twin pairs

  1. 2996863034895•21290000-1 and 2996863034895•21290000+1 on 2016-09-14 (official announcement)
  2. 3756801695685•2666669-1 and 3756801695685•2666669+1 on 2011-12-25 (official announcement)


See also

External links