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Difference between revisions of "PrimeGrid Generalized Fermat Prime Search"
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(Add new largest find from Dec 2024) |
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== Primes found == | == Primes found == | ||
| − | As of | + | As of March 2025 over {{Num|10000}} 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 | + | The largest five finds have been [[PrimeGrid GFN-20|GFN-20s]]: |
| + | * 2024-12-17: {{Kbn|+|1|3843236|1048576}} | ||
* 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}} | ||
Revision as of 10:39, 12 March 2025
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.
Contents
[hide]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 special sub-project designed to find world record primes. It was originally a variant of PrimeGrid GFN-22 (where n = 22) and searched b ≥ 846,398, the smallest b necessary such that any prime found would be larger than M51, making it a world record prime number.[2] In December 2024, after new world record prime M52 was found, the project switched to a new range, searching n = 23 for b ≥ 77,742, the minimum b needed to surpass that number.
Primes found
As of March 2025 over 10,000 primes have been found. Full list from PrimeGrid's website
The largest five finds have been GFN-20s:
- 2024-12-17: 38432361048576+1
- 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
| Miscellaneous |
| Subprojects |
|
| Completed |
| Others |
