Difference between revisions of "PrimeGrid Fermat Divisor Search"

Latest revision as of 09:13, 7 September 2021

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

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Main

Subprojects

Type Riesel :
The Riesel Problem
Riesel base 5

Completed

GFN b^2¹⁵+1

Others

[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: @@
+__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==
-Searching for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}} for 5 &le; {{Vk}} &le; 49.
+The project searched for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}}, for the following ranges:<ref name="table"/>
+* 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 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
-==Status==
+[https://www.primegrid.com/stats_div_llr.php Completed status page]
-*[https://www.primegrid.com/stats_div_llr.php Current status]
 ==Found primes==
+*2021-03-01: [[Proth prime 2 25|{{Kbn|+|25|8788628}}]]
+*2021-02-17: [[Proth prime 2 17|{{Kbn|+|17|8636199}}]]
+*2021-01-27: [[Proth prime 2 25|{{Kbn|+|25|8456828}}]]
+*2021-01-23: [[Proth prime 2 39|{{Kbn|+|39|8413422}}]]
+*2021-01-19: [[Proth prime 2 31|{{Kbn|+|31|8348000}}]]
+*2021-01-14: [[Proth prime 2 27|{{Kbn|+|27|7963247}}]], divides F(7963245)
+*2021-01-14: [[Proth prime 2 39|{{Kbn|+|39|7946769}}]]
+*2021-01-14: [[Proth prime 2 29|{{Kbn|+|29|7899985}}]]
+*2020-12-13: [[Proth prime 2 45|{{Kbn|+|45|7661004}}]]
+*2020-12-06: [[Proth prime 2 15|{{Kbn|+|15|7619838}}]]
+*2020-11-12: [[Proth prime 2 45|{{Kbn|+|45|7513661}}]]
+*2020-10-27: [[Proth prime 2 29|{{Kbn|+|29|7374577}}]]
+*2020-10-25: [[Proth prime 2 15|{{Kbn|+|15|7300254}}]]
+*2020-10-24: [[Proth prime 2 19|{{Kbn|+|19|6833086}}]]
+*2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6684941}}]]
+*2020-10-20: [[Proth prime 2 39|{{Kbn|+|39|6648997}}]]
+*2020-08-15: [[Proth prime 2 39|{{Kbn|+|39|6164630}}]]
+*2020-06-04: [[Proth prime 2 21|{{Kbn|+|21|6048861}}]]
+*2020-02-16: [[Proth prime 2 41|{{Kbn|+|41|5651731}}]]
+*2020-01-28: [[Proth prime 2 31|{{Kbn|+|31|5560820}}]]
+*2020-01-22: [[Proth prime 2 13|{{Kbn|+|13|5523860}}]], divides F(5523858)
+*2019-12-21: [[Proth prime 2 45|{{Kbn|+|45|5308037}}]]
+*2019-11-23: [[Proth prime 2 39|{{Kbn|+|39|5119458}}]]
+*2019-10-16: [[Proth prime 2 15|{{Kbn|+|15|4800315}}]]
+*2019-10-14: [[Proth prime 2 31|{{Kbn|+|31|4673544}}]]
+*2019-10-14: [[Proth prime 2 39|{{Kbn|+|39|4657951}}]]
+*2019-10-12: [[Proth prime 2 29|{{Kbn|+|29|4532463}}]]
+*2019-10-12: [[Proth prime 2 25|{{Kbn|+|25|4481024}}]]
+*2019-10-10: [[Proth prime 2 23|{{Kbn|+|23|4300741}}]]
+*2019-10-02: [[Proth prime 2 37|{{Kbn|+|37|4046360}}]]
+*2019-09-28: [[Proth prime 2 29|{{Kbn|+|29|3964697}}]]
+*2019-09-28: [[Proth prime 2 39|{{Kbn|+|39|3961129}}]]
+*2019-09-22: [[Proth prime 2 49|{{Kbn|+|49|3837090}}]]
+*2019-09-18: [[Proth prime 2 25|{{Kbn|+|25|3733144}}]]
+*2019-09-17: [[Proth prime 2 45|{{Kbn|+|45|3677787}}]]
+*2019-09-16: [[Proth prime 2 33|{{Kbn|+|33|3649810}}]]
+*2019-09-13: [[Proth prime 2 3125|{{Kbn|+|3125|3124079}}]]
+*2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2867399}}]]
+*2019-09-11: [[Proth prime 2 2187|{{Kbn|+|2187|2786802}}]]
+*2019-09-11: [[Proth prime 2 1323|{{Kbn|+|1323|2764024}}]]
+*2019-09-11: [[Proth prime 2 3125|{{Kbn|+|3125|2697651}}]]
+*2019-09-09: [[Proth prime 2 3375|{{Kbn|+|3375|2314297}}]]
+*2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2305266}}]]
+*2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2186806}}]]
+*2019-09-09: [[Proth prime 2 1323|{{Kbn|+|1323|2205832}}]]
+*2019-09-09: [[Proth prime 2 3267|{{Kbn|+|3267|2173170}}]]
+*2019-09-08: [[Proth prime 2 3125|{{Kbn|+|3125|1583223}}]]
+*2019-09-08: [[Proth prime 2 19683|{{Kbn|+|19683|2265896}}]]
+*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|2033900}}]]
+*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1868828}}]]
+*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|1797997}}]]
+*2019-09-07: [[Proth prime 2 19683|{{Kbn|+|19683|901745}}]]
+*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|493846}}]]
+*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|485845}}]]
+*2019-09-06: [[Proth prime 2 19683|{{Kbn|+|19683|366665}}]]
 ==See also==
 *[[PrimeGrid]]
-*[[Multi Reservation:20|Multi Reservation]]
 ==External links==
 *[https://www.primegrid.com/forum_thread.php?id=8778 PrimeGrid Forum]
+==References==
+<references/>
+{{Navbox PrimeGrid}}
 [[Category:PrimeGrid Fermat Divisor Search| ]]

Difference between revisions of "PrimeGrid Fermat Divisor Search"

Latest revision as of 09:13, 7 September 2021

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