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PrimeGrid Generalized Fermat Prime Search
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 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 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
| Miscellaneous |
| Subprojects |
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| Completed |
| Others |
