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Difference between revisions of "PrimeGrid Sophie Germain Search"
(→Search range: 10 trillion is 10^13, not 10^12) |
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{{C|red|2=This k-range is already done! PrimeGrid Forum thread is not current, still data for n=666666 given (''k'' ≤ 41 • 10<sup>12</sup>).}} | {{C|red|2=This k-range is already done! PrimeGrid Forum thread is not current, still data for n=666666 given (''k'' ≤ 41 • 10<sup>12</sup>).}} | ||
| − | Sophie Germain pairs take the form {{Kbn|k|1290001}}, and Twin pairs take the form {{Kbn|+|k|1290000}}. | + | 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> |
As of June 2020, the search is currently at k = 5.4 • 10<sup>12</sup>. [https://www.primegrid.com/stats_sgs_llr.php Live status] | As of June 2020, the search is currently at k = 5.4 • 10<sup>12</sup>. [https://www.primegrid.com/stats_sgs_llr.php Live status] | ||
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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]) | # {{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== | ||
Revision as of 07:24, 20 June 2020
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.
Contents
Search range
The current iteration of the project is searching for prime numbers of the form k•21290000-1, for k ≤ 1013.
This k-range is already done! 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.[1]
As of June 2020, the search is currently at k = 5.4 • 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 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
- 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)
