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Difference between revisions of "PrimeGrid Generalized Fermat Prime Search"
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| − | The '''Generalized Fermat Prime Search''' is a [[PrimeGrid]] sub-project, launched in 2009.<ref>[https://www.primegrid.com/forum_thread.php?id=5674 Welcome to the Generalized Fermat Prime Search - PrimeGrid forums]</ref> It is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers. | + | The '''Generalized Fermat Prime Search''' is a [[PrimeGrid]] sub-project, launched in 2009.<ref>[https://www.primegrid.com/forum_thread.php?id=5674 Welcome to the Generalized Fermat Prime Search - PrimeGrid forums]</ref> It is sometimes abbreviated to "Genefer" or "GFN". It is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers. |
== Purpose == | == Purpose == | ||
| − | The project is searching for primes of the form {{Kbn|+|1|b|2<sup>{{Vn}}</sup>}} where: | + | The project is currently searching for primes of the form {{Kbn|+|1|b|2<sup>{{Vn}}</sup>}} where: |
| − | * | + | * 16 ≤ {{Vn}} ≤ 22 |
* {{Vb}} ≤ 2 • 10<sup>9</sup> | * {{Vb}} ≤ 2 • 10<sup>9</sup> | ||
| − | + | [[PrimeGrid GFN-17]] (where {{Vn}} = 17) was split into two sub-projects: | |
| − | * | + | * [[PrimeGrid GFN-17 Low]], testing {{Vb}} < {{Num|42597774}}, completed |
| − | * | + | * [[PrimeGrid GFN-17 Mega]], testing {{Vb}} ≥ {{Num|42597774}} (the smallest {{Vb}} necessary to find megaprimes) |
| − | There is also "Do You Feel Lucky?", a variant of | + | There is also "Do You Feel Lucky?", a variant of [[PrimeGrid GFN-22]] (where {{Vn}} = 22) designed to find world record primes. It is currently searching {{Vb}} ≥ {{Num|846398}}, the smallest {{Vb}} necessary such that any prime found would be larger than [[M51]], making it a world record prime number. If a new world record is found outside of PrimeGrid then this project will jump up to the minimum {{Vb}} needed to surpass that number.<ref>[https://www.primegrid.com/forum_thread.php?id=8422&nowrap=true#125716 Do You Feel Lucky? - PrimeGrid forums]</ref> |
== Primes found == | == Primes found == | ||
| − | As of July 2023 over | + | As of July 2023 over {{Num|7000}} primes have been found. [https://www.primegrid.com/primes/primes.php?project=GFN&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= Full list from PrimeGrid's website] |
| − | The largest four finds have been GFN- | + | The largest four finds have been [[PrimeGrid GFN-20]]: |
* 2022-09-24: {{Kbn|+|1|1963736|1048576}} | * 2022-09-24: {{Kbn|+|1|1963736|1048576}} | ||
* 2022-08-09: {{Kbn|+|1|1951734|1048576}} | * 2022-08-09: {{Kbn|+|1|1951734|1048576}} | ||
| Line 23: | Line 23: | ||
== Status == | == Status == | ||
[https://www.primegrid.com/stats_genefer.php Live status at PrimeGrid] | [https://www.primegrid.com/stats_genefer.php Live status at PrimeGrid] | ||
| + | |||
| + | == Completed == | ||
| + | * 2022-01: [[PrimeGrid GFN-17 Low]], testing {{Vb}} < {{Num|42597774}} ({{HistLink|2021-11-14|P#9796}}: Forum / {{HistLink|2022-01-23|P#9796#153518}}: Post) | ||
| + | * 2023-11-15: [[PrimeGrid GFN-15]] was terminated at {{Vb}} = {{Num|460000000}}. ({{HistLink|2023-09-14|P#10333}}: Forum / {{HistLink|2023-11-08|P#10333#166430}}: Post) | ||
== References == | == References == | ||
Latest revision as of 06:38, 29 December 2023
The Generalized Fermat Prime Search is a PrimeGrid sub-project, launched in 2009.[1] It is sometimes abbreviated to "Genefer" or "GFN". It is searching for Generalized Fermat prime numbers.
Purpose
The project is currently searching for primes of the form b2n+1 where:
- 16 ≤ n ≤ 22
- b ≤ 2 • 109
PrimeGrid GFN-17 (where n = 17) was split into two sub-projects:
- PrimeGrid GFN-17 Low, testing b < 42,597,774, completed
- PrimeGrid GFN-17 Mega, testing b ≥ 42,597,774 (the smallest b necessary to find megaprimes)
There is also "Do You Feel Lucky?", a variant of PrimeGrid GFN-22 (where n = 22) designed to find world record primes. It is currently searching b ≥ 846,398, the smallest b necessary such that any prime found would be larger than M51, making it a world record prime number. If a new world record is found outside of PrimeGrid then this project will jump up to the minimum b needed to surpass that number.[2]
Primes found
As of July 2023 over 7,000 primes have been found. Full list from PrimeGrid's website
The largest four finds have been PrimeGrid GFN-20:
- 2022-09-24: 19637361048576+1
- 2022-08-09: 19517341048576+1
- 2018-10-31: 10590941048576+1
- 2017-08-29: 9194441048576+1
Status
Completed
- 2022-01: PrimeGrid GFN-17 Low, testing b < 42,597,774 (2021-11-14: Forum / 2022-01-23: Post)
- 2023-11-15: PrimeGrid GFN-15 was terminated at b = 460,000,000. (2023-09-14: Forum / 2023-11-08: Post)
References
PrimeGrid
| Miscellaneous |
| Subprojects |
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| Completed |
| Others |
