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The '''Sophie Germain Search''' is a [[PrimeGrid]] sub-project searching for [[Sophie Germain prime|Sophie Germain]] and [[Twin prime]] pairs. It was launched in 2009 as a successor to the Twin Prime Search sub-project.
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The '''Sophie Germain Search''' was a [[PrimeGrid]] sub-project searching for [[Sophie Germain prime|Sophie Germain]] and [[Twin prime]] pairs. It was launched in 2009 as a successor to the Twin Prime Search sub-project. The project ended in December 2023.<ref>[https://www.primegrid.com/forum_thread.php?id=10333#165213 PPS-Sieve, PPS-MEGA, GFN-15, SGS, and AP27 are shutting down - PrimeGrid Forums]</ref>
  
 
==Search range==
 
==Search range==
The current iteration of the project is searching for prime numbers of the form k × 2<sup>1290000</sup> - 1, for ''k'' ≤ 10 trillion. Sophie Germain pairs take the form k × 2<sup>1290001</sup> - 1, and Twin pairs take the form k × 2<sup>1290000</sup> + 1.
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The most recent iteration of the project searched for prime numbers of the form {{Kbn|k|1290000}}, for ''k'' ≤ 10<sup>13</sup>.  
  
As of June 2020, the search is currently at k = 5.4 trillion. [https://www.primegrid.com/stats_sgs_llr.php Live status]
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Sophie Germain pairs take the form {{Kbn|k|1290001}} or {{Kbn|k|1289999}}, and Twin pairs take the form {{Kbn|+|k|1290000}}.<ref>[https://www.primegrid.com/forum_thread.php?id=1450&nowrap=true#70736 PrimeGrid forum post - 8 Nov 2013]</ref>
  
The first version of the project searched for prime numbers k × 2<sup>n</sup> - 1 for 666,666 ≤ ''n'' ≤ 666,691 with varying ranges of ''k'' values up to 38.5 trillion.
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The project reached its end point, ''k'' = 10<sup>13</sup>, in December 2023. ([https://www.primegrid.com/stats_sgs_llr.php Live status])
  
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The first version of the project searched for prime numbers {{Kbn|k|n}} for 666,666 ≤ ''n'' ≤ 666,691 with varying ranges of ''k'' values up to 38.5 • 10<sup>12</sup>.
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{{C|red|2=PrimeGrid Forum thread is not current, still data for n=666666 given (''k'' ≤ 41 • 10<sup>12</sup>).}}
 
==Found primes==
 
==Found primes==
As of June 2020 the project has found over 8200 primes, with 2 Sophie Germain pairs and 2 Twin pairs.
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The project found over 12200 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===
 
===Sophie Germain pairs===
# {{Kbn|2618163402417|1290000}} and {{Kbn|2618163402417|1290001}} on 2016-02-29, [https://www.primegrid.com/download/SGS_2618163402417_1290000.pdf official announcement]
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# [[Riesel prime 2618163402417|{{Kbn|2618163402417|1290000}}]] and [[Riesel prime 2618163402417|{{Kbn|2618163402417|1290001}}]] on 2016-02-29 ([https://www.primegrid.com/download/SGS_2618163402417_1290000.pdf official announcement])
# {{Kbn|18543637900515|666667}} and {{Kbn|18543637900515|666668}} on 2012-04-09, [https://www.primegrid.com/download/SGS-666667.pdf official announcement]
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# [[Riesel prime 18543637900515|{{Kbn|18543637900515|666667}}]] and [[Riesel prime 18543637900515|{{Kbn|18543637900515|666668}}]] on 2012-04-09 ([https://www.primegrid.com/download/SGS-666667.pdf official announcement])
  
 
===Twin pairs===
 
===Twin pairs===
# {{Kbn|2996863034895|1290000}} and {{Kbn|+|2996863034895|1290000}} on 2016-09-14, [https://www.primegrid.com/download/twin-1290000.pdf official announcement]
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# {{T5000|122213|{{Kbn|2996863034895|1290000}}}} and {{T5000|122214|{{Kbn|+|2996863034895|1290000}}}} on 2016-09-14 ([https://www.primegrid.com/download/twin-1290000.pdf official announcement])
# {{Kbn|3756801695685|666669}} and {{Kbn|+|3756801695685|666669}} on 2011-12-25, [https://www.primegrid.com/download/twin-666669.pdf official announcement]
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# {{T5000|103792|{{Kbn|3756801695685|666669}}}} and {{T5000|103791|{{Kbn|+|3756801695685|666669}}}} on 2011-12-25 ([https://www.primegrid.com/download/twin-666669.pdf official announcement])
  
==History==
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==References==
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<references/>
  
 
==See also==
 
==See also==
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* [https://www.primegrid.com/primes/primes.php?project=SGS Full list of primes found by project]
 
* [https://www.primegrid.com/primes/primes.php?project=SGS Full list of primes found by project]
  
[[Category:PrimeGrid]]
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{{Navbox PrimeGrid}}
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[[Category:PrimeGrid|Sophie Germain Search]]

Latest revision as of 15:13, 16 December 2023

The Sophie Germain Search was 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 ended in December 2023.[1]

Search range

The most recent iteration of the project searched for prime numbers of the form k•21290000-1, for k ≤ 1013.

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

The project reached its end point, k = 1013, in December 2023. (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.

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

Found primes

The project found over 12200 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)

References

See also

External links

PrimeGrid