Difference between revisions of "PrimeGrid Fermat Divisor Search"

Revision as of 03:54, 18 June 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

Completed status page

Found primes

2021-03-01: 25•2^8788628+1
2021-02-17: 17•2^8636199+1
2021-01-27: 25•2^8456828+1
2021-01-23: 39•2^8413422+1
2021-01-19: 31•2^8348000+1
2021-01-14: 27•2^7963247+1, divides F(7963245)
2021-01-14: 39•2^7946769+1
2021-01-14: 29•2^7899985+1
2020-12-13: 45•2^7661004+1
2020-12-06: 15•2^7619838+1
2020-11-12: 45•2^7513661+1
2020-10-27: 29•2^7374577+1
2020-10-25: 15•2^7300254+1
2020-10-24: 19•2^6833086+1
2020-10-20: 39•2^6684941+1
2020-10-20: 39•2^6648997+1
2020-08-15: 39•2^6164630+1
2020-06-04: 21•2^6048861+1
2020-02-16: 41•2^5651731+1
2020-01-28: 31•2^5560820+1
2020-01-22: 13•2^5523860+1, divides F(5523858)
2019-12-21: 45•2^5308037+1
2019-11-23: 39•2^5119458+1
2019-10-16: 15•2^4800315+1
2019-10-14: 31•2^4673544+1
2019-10-14: 39•2^4657951+1
2019-10-12: 29•2^4532463+1
2019-10-12: 25•2^4481024+1
2019-10-10: 23•2^4300741+1
2019-10-02: 37•2^4046360+1
2019-09-28: 29•2^3964697+1
2019-09-28: 39•2^3961129+1
2019-09-22: 49•2^3837090+1
2019-09-18: 25•2^3733144+1
2019-09-17: 45•2^3677787+1
2019-09-16: 33•2^3649810+1
2019-09-13: 3125•2^3124079+1
2019-09-11: 3125•2^2867399+1
2019-09-11: 2187•2^2786802+1
2019-09-11: 1323•2^2764024+1
2019-09-11: 3125•2^2697651+1
2019-09-09: 3375•2^2314297+1
2019-09-09: 3267•2^2305266+1
2019-09-09: 1323•2^2186806+1
2019-09-09: 1323•2^2205832+1
2019-09-09: 3267•2^2173170+1
2019-09-08: 3125•2^1583223+1
2019-09-08: 19683•2^2265896+1
2019-09-07: 19683•2^2033900+1
2019-09-07: 19683•2^1868828+1
2019-09-07: 19683•2^1797997+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

References

External links

PrimeGrid Forum

[table-1] 1.0 ^1.1 Fermat Divisor Search, Message 149792 - PrimeGrid Forums

[2] What primes can be Fermat divisors? - PrimeGrid Forums

[3] Fermat Divisor Search, Message 132677 - PrimeGrid Forums

[1]

[2]

[3]

@@ Line 1: / Line 1: @@
-'''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>
+'''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==
@@ Line 6: / Line 6: @@
 * 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}} = 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}} = 19683 for {{Vn}} ≤ 4,000,000
@@ Line 33: / Line 33: @@
 *2020-02-16: [[Proth prime 41|{{Kbn|+|41|5651731}}]]
 *2020-01-28: [[Proth prime 31|{{Kbn|+|31|5560820}}]]
-*2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]]
+*2020-01-22: [[Proth prime 13|{{Kbn|+|13|5523860}}]], divides F(5523858)
 *2019-12-21: [[Proth prime 45|{{Kbn|+|45|5308037}}]]
 *2019-11-23: [[Proth prime 39|{{Kbn|+|39|5119458}}]]

Difference between revisions of "PrimeGrid Fermat Divisor Search"

Revision as of 03:54, 18 June 2021

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