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Difference between revisions of "PrimeGrid Sophie Germain Search"
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===Sophie Germain pairs=== | ===Sophie Germain pairs=== | ||
# {{T5000|121330|{{Kbn|2618163402417|1290000}}}} and {{T5000|121331|{{Kbn|2618163402417|1290001}}}} on 2016-02-29 ([https://www.primegrid.com/download/SGS_2618163402417_1290000.pdf official announcement]) | # {{T5000|121330|{{Kbn|2618163402417|1290000}}}} and {{T5000|121331|{{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=== | ||
Revision as of 10:43, 16 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 ≤ 10 trillion. Sophie Germain pairs take the form k × 21290001 - 1, and Twin pairs take the form k × 21290000 + 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
- 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)
