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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 searching for Generalized Fermat prime numbers.
Contents
Purpose
The project is searching for primes of the form b2n+1 where:
- 15 ≤ n ≤ 22
- b ≤ 2 • 109
"Genefer 17" (where n = 17) was split into two sub-projects:
- "Genefer 17 Low", testing b < 42,597,774, completed.
- "Genefer 17 Mega", testing b ≥ 42,597,774 (the smallest b necessary to find megaprimes)
There is also "Do You Feel Lucky?", a variant of Genefer 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 GFN-20s:
- 2022-09-24: 19637361048576+1
- 2022-08-09: 19517341048576+1
- 2018-10-31: 10590941048576+1
- 2017-08-29: 9194441048576+1
Status
References
| Miscellaneous |
| Subprojects |
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| Completed |
| Others |
