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Difference between revisions of "PrimeGrid Fermat Divisor Search"
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| − | '''Fermat Divisor Search''' was a [[PrimeGrid]] project searching for large [[Fermat divisor]]s. It began in September 2019, and ended in April 2021.<ref name="table">https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#149792</ref> | + | __TOC__ |
| + | '''Fermat Divisor Search''' was a [[PrimeGrid]] project searching for large [[Fermat divisor]]s. It began in September 2019, and ended in April 2021.<ref name="table">[https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#149792 Fermat Divisor Search, Message 149792 - PrimeGrid Forums]</ref> | ||
==Purpose== | ==Purpose== | ||
| Line 6: | Line 7: | ||
* 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions: | * 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions: | ||
**{{Vk}} = 9 and 27 did not search even {{Vn}}-values, because they cannot produce Fermat divisors.<ref>[https://www.primegrid.com/forum_thread.php?id=8783 What primes can be Fermat divisors? - PrimeGrid Forums]</ref> | **{{Vk}} = 9 and 27 did not search even {{Vn}}-values, because they cannot produce Fermat divisors.<ref>[https://www.primegrid.com/forum_thread.php?id=8783 What primes can be Fermat divisors? - PrimeGrid Forums]</ref> | ||
| − | * {{Vk}} = 1323, 2187, 3267 for even<ref>https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#132677</ref> {{Vn}} ≤ 3,322,000 | + | * {{Vk}} = 1323, 2187, 3267 for even<ref>[https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#132677 Fermat Divisor Search, Message 132677 - PrimeGrid Forums]</ref> {{Vn}} ≤ 3,322,000 |
* {{Vk}} = 3125, 3375 for {{Vn}} ≤ 3,322,000 | * {{Vk}} = 3125, 3375 for {{Vn}} ≤ 3,322,000 | ||
* {{Vk}} = 19683 for {{Vn}} ≤ 4,000,000 | * {{Vk}} = 19683 for {{Vn}} ≤ 4,000,000 | ||
| Line 13: | Line 14: | ||
==Found primes== | ==Found primes== | ||
| − | *2021-03-01: [[Proth prime 25|{{Kbn|+|25|8788628}}]] | + | *2021-03-01: [[Proth prime 2 25|{{Kbn|+|25|8788628}}]] |
| − | *2021-02-17: [[Proth prime 17|{{Kbn|+|17|8636199}}]] | + | *2021-02-17: [[Proth prime 2 17|{{Kbn|+|17|8636199}}]] |
| − | *2021-01-27: [[Proth prime 25|{{Kbn|+|25|8456828}}]] | + | *2021-01-27: [[Proth prime 2 25|{{Kbn|+|25|8456828}}]] |
| − | *2021-01-23: [[Proth prime 39|{{Kbn|+|39|8413422}}]] | + | *2021-01-23: [[Proth prime 2 39|{{Kbn|+|39|8413422}}]] |
| − | *2021-01-19: [[Proth prime 31|{{Kbn|+|31|8348000}}]] | + | *2021-01-19: [[Proth prime 2 31|{{Kbn|+|31|8348000}}]] |
| − | *2021-01-14: [[Proth prime 27|{{Kbn|+|27|7963247}}]], divides F(7963245) | + | *2021-01-14: [[Proth prime 2 27|{{Kbn|+|27|7963247}}]], divides F(7963245) |
| − | *2021-01-14: [[Proth prime 39|{{Kbn|+|39|7946769}}]] | + | *2021-01-14: [[Proth prime 2 39|{{Kbn|+|39|7946769}}]] |
| − | *2021-01-14: [[Proth prime 29|{{Kbn|+|29|7899985}}]] | + | *2021-01-14: [[Proth prime 2 29|{{Kbn|+|29|7899985}}]] |
| − | *2020-12-13: [[Proth prime 45|{{Kbn|+|45|7661004}}]] | + | *2020-12-13: [[Proth prime 2 45|{{Kbn|+|45|7661004}}]] |
| − | *2020-12-06: [[Proth prime 15|{{Kbn|+|15|7619838}}]] | + | *2020-12-06: [[Proth prime 2 15|{{Kbn|+|15|7619838}}]] |
| − | *2020-11-12: [[Proth prime 45|{{Kbn|+|45|7513661}}]] | + | *2020-11-12: [[Proth prime 2 45|{{Kbn|+|45|7513661}}]] |
| − | *2020-10-27: [[Proth prime 29|{{Kbn|+|29|7374577}}]] | + | *2020-10-27: [[Proth prime 2 29|{{Kbn|+|29|7374577}}]] |
| − | *2020-10-25: [[Proth prime 15|{{Kbn|+|15|7300254}}]] | + | *2020-10-25: [[Proth prime 2 15|{{Kbn|+|15|7300254}}]] |
| − | *2020-10-24: [[Proth prime 19|{{Kbn|+|19|6833086}}]] | + | *2020-10-24: [[Proth prime 2 19|{{Kbn|+|19|6833086}}]] |
| − | *2020-10-20: [[Proth prime 39|{{Kbn|+|39|6684941}}]] | + | *2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6684941}}]] |
| − | *2020-10-20: [[Proth prime 39|{{Kbn|+|39|6648997}}]] | + | *2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6648997}}]] |
| − | *2020-08-15: [[Proth prime 39|{{Kbn|+|39|6164630}}]] | + | *2020-08-15: [[Proth prime 2 39|{{Kbn|+|39|6164630}}]] |
| − | *2020-06-04: [[Proth prime 21|{{Kbn|+|21|6048861}}]] | + | *2020-06-04: [[Proth prime 2 21|{{Kbn|+|21|6048861}}]] |
| − | *2020-02-16: [[Proth prime 41|{{Kbn|+|41|5651731}}]] | + | *2020-02-16: [[Proth prime 2 41|{{Kbn|+|41|5651731}}]] |
| − | *2020-01-28: [[Proth prime 31|{{Kbn|+|31|5560820}}]] | + | *2020-01-28: [[Proth prime 2 31|{{Kbn|+|31|5560820}}]] |
| − | *2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]] | + | *2020-01-22: [[Proth prime 2 13|{{Kbn|+|13|5523860}}]], divides F(5523858) |
| − | *2019-12-21: [[Proth prime 45|{{Kbn|+|45|5308037}}]] | + | *2019-12-21: [[Proth prime 2 45|{{Kbn|+|45|5308037}}]] |
| − | *2019-11-23: [[Proth prime 39|{{Kbn|+|39|5119458}}]] | + | *2019-11-23: [[Proth prime 2 39|{{Kbn|+|39|5119458}}]] |
| − | *2019-10-16: [[Proth prime 15|{{Kbn|+|15|4800315}}]] | + | *2019-10-16: [[Proth prime 2 15|{{Kbn|+|15|4800315}}]] |
| − | *2019-10-14: [[Proth prime 31|{{Kbn|+|31|4673544}}]] | + | *2019-10-14: [[Proth prime 2 31|{{Kbn|+|31|4673544}}]] |
| − | *2019-10-14: [[Proth prime 39|{{Kbn|+|39|4657951}}]] | + | *2019-10-14: [[Proth prime 2 39|{{Kbn|+|39|4657951}}]] |
| − | *2019-10-12: [[Proth prime 29|{{Kbn|+|29|4532463}}]] | + | *2019-10-12: [[Proth prime 2 29|{{Kbn|+|29|4532463}}]] |
| − | *2019-10-12: [[Proth prime 25|{{Kbn|+|25|4481024}}]] | + | *2019-10-12: [[Proth prime 2 25|{{Kbn|+|25|4481024}}]] |
| − | *2019-10-10: [[Proth prime 23|{{Kbn|+|23|4300741}}]] | + | *2019-10-10: [[Proth prime 2 23|{{Kbn|+|23|4300741}}]] |
| − | *2019-10-02: [[Proth prime 37|{{Kbn|+|37|4046360}}]] | + | *2019-10-02: [[Proth prime 2 37|{{Kbn|+|37|4046360}}]] |
| − | *2019-09-28: [[Proth prime 29|{{Kbn|+|29|3964697}}]] | + | *2019-09-28: [[Proth prime 2 29|{{Kbn|+|29|3964697}}]] |
| − | *2019-09-28: [[Proth prime 39|{{Kbn|+|39|3961129}}]] | + | *2019-09-28: [[Proth prime 2 39|{{Kbn|+|39|3961129}}]] |
| − | *2019-09-22: [[Proth prime 49|{{Kbn|+|49|3837090}}]] | + | *2019-09-22: [[Proth prime 2 49|{{Kbn|+|49|3837090}}]] |
| − | *2019-09-18: [[Proth prime 25|{{Kbn|+|25|3733144}}]] | + | *2019-09-18: [[Proth prime 2 25|{{Kbn|+|25|3733144}}]] |
| − | *2019-09-17: [[Proth prime 45|{{Kbn|+|45|3677787}}]] | + | *2019-09-17: [[Proth prime 2 45|{{Kbn|+|45|3677787}}]] |
| − | *2019-09-16: [[Proth prime 33|{{Kbn|+|33|3649810}}]] | + | *2019-09-16: [[Proth prime 2 33|{{Kbn|+|33|3649810}}]] |
| − | *2019-09-13: [[Proth prime 3125|{{Kbn|+|3125|3124079}}]] | + | *2019-09-13: [[Proth prime 2 3125|{{Kbn|+|3125|3124079}}]] |
| − | *2019-09-11: [[Proth prime 3125|{{Kbn|+|3125|2867399}}]] | + | *2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2867399}}]] |
| − | *2019-09-11: [[Proth prime 2187|{{Kbn|+|2187|2786802}}]] | + | *2019-09-11: [[Proth prime 2 2187|{{Kbn|+|2187|2786802}}]] |
| − | *2019-09-11: [[Proth prime 1323|{{Kbn|+|1323|2764024}}]] | + | *2019-09-11: [[Proth prime 2 1323|{{Kbn|+|1323|2764024}}]] |
| − | *2019-09-11: [[Proth prime 3125|{{Kbn|+|3125|2697651}}]] | + | *2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2697651}}]] |
| − | *2019-09-09: [[Proth prime 3375|{{Kbn|+|3375|2314297}}]] | + | *2019-09-09: [[Proth prime 2 3375|{{Kbn|+|3375|2314297}}]] |
| − | *2019-09-09: [[Proth prime 3267|{{Kbn|+|3267|2305266}}]] | + | *2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2305266}}]] |
| − | *2019-09-09: [[Proth prime 1323|{{Kbn|+|1323|2186806}}]] | + | *2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2186806}}]] |
| − | *2019-09-09: [[Proth prime 1323|{{Kbn|+|1323|2205832}}]] | + | *2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2205832}}]] |
| − | *2019-09-09: [[Proth prime 3267|{{Kbn|+|3267|2173170}}]] | + | *2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2173170}}]] |
| − | *2019-09-08: [[Proth prime 3125|{{Kbn|+|3125|1583223}}]] | + | *2019-09-08: [[Proth prime 2 3125|{{Kbn|+|3125|1583223}}]] |
| − | *2019-09-08: [[Proth prime 19683|{{Kbn|+|19683|2265896}}]] | + | *2019-09-08: [[Proth prime 2 19683|{{Kbn|+|19683|2265896}}]] |
| − | *2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|2033900}}]] | + | *2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|2033900}}]] |
| − | *2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|1868828}}]] | + | *2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1868828}}]] |
| − | *2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|1797997}}]] | + | *2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1797997}}]] |
| − | *2019-09-07: [[Proth prime 19683|{{Kbn|+|19683|901745}}]] | + | *2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|901745}}]] |
| − | *2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|493846}}]] | + | *2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|493846}}]] |
| − | *2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|485845}}]] | + | *2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|485845}}]] |
| − | *2019-09-06: [[Proth prime 19683|{{Kbn|+|19683|366665}}]] | + | *2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|366665}}]] |
==See also== | ==See also== | ||
| − | |||
*[[PrimeGrid]] | *[[PrimeGrid]] | ||
| − | |||
| − | |||
| − | |||
==External links== | ==External links== | ||
*[https://www.primegrid.com/forum_thread.php?id=8778 PrimeGrid Forum] | *[https://www.primegrid.com/forum_thread.php?id=8778 PrimeGrid Forum] | ||
| + | ==References== | ||
| + | <references/> | ||
| + | {{Navbox PrimeGrid}} | ||
[[Category:PrimeGrid Fermat Divisor Search| ]] | [[Category:PrimeGrid Fermat Divisor Search| ]] | ||
Latest revision as of 09:13, 7 September 2021
Fermat Divisor Search was a PrimeGrid project searching for large Fermat divisors. It began in September 2019, and ended in April 2021.[1]
Purpose
The project searched for Fermat divisors of the form k•2n+1, for the following ranges:[1]
- 5 ≤ k ≤ 49 for n ≤ 9,000,000, with two exceptions:
- k = 9 and 27 did not search even n-values, because they cannot produce Fermat divisors.[2]
- k = 1323, 2187, 3267 for even[3] n ≤ 3,322,000
- k = 3125, 3375 for n ≤ 3,322,000
- k = 19683 for n ≤ 4,000,000
Found primes
- 2021-03-01: 25•28788628+1
- 2021-02-17: 17•28636199+1
- 2021-01-27: 25•28456828+1
- 2021-01-23: 39•28413422+1
- 2021-01-19: 31•28348000+1
- 2021-01-14: 27•27963247+1, divides F(7963245)
- 2021-01-14: 39•27946769+1
- 2021-01-14: 29•27899985+1
- 2020-12-13: 45•27661004+1
- 2020-12-06: 15•27619838+1
- 2020-11-12: 45•27513661+1
- 2020-10-27: 29•27374577+1
- 2020-10-25: 15•27300254+1
- 2020-10-24: 19•26833086+1
- 2020-10-20: 39•26684941+1
- 2020-10-20: 39•26648997+1
- 2020-08-15: 39•26164630+1
- 2020-06-04: 21•26048861+1
- 2020-02-16: 41•25651731+1
- 2020-01-28: 31•25560820+1
- 2020-01-22: 13•25523860+1, divides F(5523858)
- 2019-12-21: 45•25308037+1
- 2019-11-23: 39•25119458+1
- 2019-10-16: 15•24800315+1
- 2019-10-14: 31•24673544+1
- 2019-10-14: 39•24657951+1
- 2019-10-12: 29•24532463+1
- 2019-10-12: 25•24481024+1
- 2019-10-10: 23•24300741+1
- 2019-10-02: 37•24046360+1
- 2019-09-28: 29•23964697+1
- 2019-09-28: 39•23961129+1
- 2019-09-22: 49•23837090+1
- 2019-09-18: 25•23733144+1
- 2019-09-17: 45•23677787+1
- 2019-09-16: 33•23649810+1
- 2019-09-13: 3125•23124079+1
- 2019-09-11: 3125•22867399+1
- 2019-09-11: 2187•22786802+1
- 2019-09-11: 1323•22764024+1
- 2019-09-11: 3125•22697651+1
- 2019-09-09: 3375•22314297+1
- 2019-09-09: 3267•22305266+1
- 2019-09-09: 1323•22186806+1
- 2019-09-09: 1323•22205832+1
- 2019-09-09: 3267•22173170+1
- 2019-09-08: 3125•21583223+1
- 2019-09-08: 19683•22265896+1
- 2019-09-07: 19683•22033900+1
- 2019-09-07: 19683•21868828+1
- 2019-09-07: 19683•21797997+1
- 2019-09-07: 19683•2901745+1
- 2019-09-06: 19683•2493846+1
- 2019-09-06: 19683•2485845+1
- 2019-09-06: 19683•2366665+1
See also
External links
References
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