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Difference between revisions of "PrimeGrid Sophie Germain Search"
(Created a page for PrimeGrid's SGS search. Needs inclusion of the n=666666-666691 search that happened before this) |
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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> | |
| − | The '''Sophie Germain Search''' | ||
==Search range== | ==Search range== | ||
| − | The | + | The most recent iteration of the project searched for prime numbers of the form {{Kbn|k|1290000}}, for ''k'' ≤ 10<sup>13</sup>. |
| − | + | 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 project reached its end point, ''k'' = 10<sup>13</sup>, in December 2023. ([https://www.primegrid.com/stats_sgs_llr.php Live status]) | ||
| + | |||
| + | 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>. | ||
| + | |||
| + | {{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== | ||
| − | + | 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 | + | # [[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]) |
| + | # [[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 | + | # {{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]) |
| + | # {{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]) | ||
| − | == | + | ==References== |
| + | <references/> | ||
==See also== | ==See also== | ||
| − | + | * [[Sophie Germain prime]] | |
| + | * [[Twin prime]] | ||
| + | * [[PrimeGrid]] | ||
==External links== | ==External links== | ||
| − | [https://www.primegrid.com/forum_thread.php?id=1450 Sophie Germain Prime Search forum introduction thread] | + | * [https://www.primegrid.com/forum_thread.php?id=1450 Sophie Germain Prime Search forum introduction thread] |
| + | * [https://www.primegrid.com/primes/primes.php?project=SGS Full list of primes found by project] | ||
| − | [[Category:PrimeGrid]] | + | {{Navbox PrimeGrid}} |
| + | [[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]
Contents
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
- 2618163402417•21290000-1 and 2618163402417•21290001-1 on 2016-02-29 (official announcement)
- 18543637900515•2666667-1 and 18543637900515•2666668-1 on 2012-04-09 (official announcement)
Twin pairs
- 2996863034895•21290000-1 and 2996863034895•21290000+1 on 2016-09-14 (official announcement)
- 3756801695685•2666669-1 and 3756801695685•2666669+1 on 2011-12-25 (official announcement)
References
See also
External links
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