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Create the page "Fermat prime" on this wiki! See also the search results found.

Page title matches

  • Generalized Fermat prime
    ...'generalized Fermat prime''' is a [[generalized Fermat number]] which is [[prime]]. *[[Wikipedia:Fermat_number#Generalized_Fermat_primes|Generalized Fermat prime]]
    372 bytes (49 words) - 13:35, 6 March 2019
  • PrimeGrid Generalized Fermat Prime Search
    ...t is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers. ...hat 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 proje
    2 KB (310 words) - 06:38, 29 December 2023

Page text matches

  • Marin Mersenne
    Mersenne is remembered today thanks to his association with the [[Mersenne prime]]s. The [[Mersenne twister]], named for him, is frequently used in computer ...for exchange of information. These include such notables as: [[Pierre de Fermat]], Pascal, Gassendi, Roberval, Beaugrand, Huygens, Pell, Galileo and Torric
    11 KB (1,582 words) - 01:17, 15 January 2024
  • Fermat number
    In [[mathematics]], a '''Fermat number''', named after [[Pierre de Fermat]] who first studied them, is a positive integer of the form where {{Vn}} is a [[non-negative]] [[integer]]. The first eight Fermat numbers are (see {{OEIS|l|A000215}}):
    12 KB (1,913 words) - 14:35, 9 August 2021
  • Derrick Henry Lehmer
    ...rsenne prime]]s <math>2^p{-}1</math>, extending its application to all odd prime exponents ''p'', and enabling him to add his name to the test so that it is ...called 'Lehmer Numbers'. He also clarified and extended Lucas' use of the Fermat congruence in primality testing, making its use widely known and in a paper
    6 KB (1,033 words) - 01:13, 15 January 2024
  • Cunningham project
    ...the form <math>2kn+1</math>. Note that when the exponent <math>n</math> is prime, algebraic and Aurifeuillian factors are not possible, except for the trivi ...of the form <math>2kn+1</math>, <math>b \ge 2</math> and <math>n</math> is prime, except when <math>n</math> is a factor of <math>x-1</math>. In such cases,
    7 KB (1,150 words) - 23:48, 19 April 2023
  • Lucas-Lehmer test
    ...e last stage in the procedure employed by [[GIMPS]] for finding [[Mersenne prime]]s. Previous stages try to find factors, as explained on [[GIMPS factoring ...lete proof that this was not only true when p = 1 (mod 4), but for all odd prime exponents. The test therefore takes its name from the two mathematicians wh
    20 KB (3,572 words) - 14:30, 17 February 2019
  • Mlucas
    ...hmer test]]s of prime-exponent [[Mersenne number]]s, and Pépin tests of [[Fermat number]]s. It is written by [[Ernst Mayer]] using C programming language an ...es not impose prize-sharing rules, should a user be lucky as to find a new prime eligible for the monetary prize offered by the [[Electronic Frontier Founda
    1 KB (198 words) - 07:28, 22 August 2019
  • Conjectures 'R Us
    ...or a combination of algebraic and trivial factor(s), or make [[Generalized Fermat number]]'s. ...557 &lt; {{Vk}} &lt; 271129 has been extensively tested by the [[PrimeGrid Prime Sierpiński Problem]] and the [[PrimeGrid Extended Sierpiński Problem]] pr
    3 KB (503 words) - 02:20, 1 May 2024
  • Elliptic curve method
    ...first six prime numbers multiplied together. If we multiply the first 2000 prime numbers together we get a huge number that has lots and lots of divisors. T ...at we work modulo a prime <math>p</math> (this will be an a-priori unknown prime factor of <math>N</math>). Given the set of points for which '''(1)''' hold
    19 KB (3,181 words) - 22:27, 6 July 2023
  • Rho factorization method
    When N = pq where p and q are [[coprime]] but not necessarily [[prime]], we will see that after about <math>\sqrt p</math> elements the sequence ...s was invented by Richard Brent in 1980 who used it to factor the eighth [[Fermat number]].
    3 KB (558 words) - 10:28, 6 February 2019
  • Primality test
    .... When the number is declared composite, the algorithm does not reveal the prime [[factor]]s. That is the job of the [[Factorization|factorization methods]] ...the confidence grows, but we cannot be completely sure that the number is prime until a primality test (which is far slower than a probable primality test
    3 KB (501 words) - 05:20, 3 August 2021
  • Primality testing program
    ...ne number]]s<br/>a &times; b<sup>n</sup>±c (only factoring and [[probable prime|PRP]]-testing) | [[generalized Fermat number]]s
    2 KB (314 words) - 21:23, 29 August 2019
  • Pépin's test
    '''Pépin's test''' is mainly used for proving the primality of [[Fermat number]]s, but it is of no help for finding the factors of such numbers. ...be used for proving the primality of other numbers, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k
    2 KB (401 words) - 14:40, 6 March 2019
  • Probable prime
    ...an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}} ...an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers. Different types of probable primes have different specific condi
    2 KB (232 words) - 07:28, 12 March 2024
  • GIMPS factoring and sieving
    ...o do the Lucas-Lehmer Test; in fact, over 60% of [[Mersenne number]]s with prime exponents are eliminated from consideration as possible primes this way, so ...te numbers, it may make more sense to test the remaining 5% along with any prime potential factors by the power-mod algorithm than to do further sieving.
    6 KB (962 words) - 10:08, 7 March 2019
  • LLR
    ...ith |{{V|c}}| ≠ 1 or {{V|k}} > {{Vb}}<sup>{{Vn}}</sup> can be [[probable prime|PRP]]-tested. ...s and Wagstaff numbers (2<sup>{{V|p}}</sup>+1)/3. The latter uses a strong Fermat PRP-test and the [[Vrba-Reix algorithm]].
    2 KB (300 words) - 22:00, 16 December 2023
  • P-1 factorization method
    It is based in the Fermat's Little Theorem that states that: Let ''p'' be a prime which does not divide the integer ''a'', then <math>a^{p-1}\equiv 1 \mbox{(
    5 KB (814 words) - 01:35, 12 March 2019
  • Brent-Suyama extension
    ...oduct of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. ...tage 2 would then compute T=S<sup>q</sup> = 3<sup>E*q</sup> for successive prime q in the range (B1,B2]. Then p | T-1 if p-1 | q*E.
    2 KB (421 words) - 11:51, 28 January 2019
  • Fermat pseudoprimality test
    The '''Fermat pseudoprimality test''' is based on the Fermat Little Theorem that states: where ''p'' is a [[prime]] number and ''a'' is not multiple of <math>p</math>.
    1 KB (164 words) - 10:56, 6 February 2019
  • Miller-Rabin pseudoprimality test
    The '''Miller-Rabin pseudoprimality test''' is based in two facts for prime numbers: *The Fermat Little Theorem that states: <math>a^{p-1}\equiv 1\,\pmod p</math>.
    3 KB (432 words) - 15:33, 28 January 2019
  • GeneferCUDA
    ...DAGenefer''') is a program for finding large probable [[generalized Fermat prime]]s.
    362 bytes (48 words) - 09:20, 29 January 2019
  • Generalized Fermat prime
    ...'generalized Fermat prime''' is a [[generalized Fermat number]] which is [[prime]]. *[[Wikipedia:Fermat_number#Generalized_Fermat_primes|Generalized Fermat prime]]
    372 bytes (49 words) - 13:35, 6 March 2019
  • Generalized Fermat number
    There are different kinds of '''generalized [[Fermat number]]s'''. ...2^{2p^n}+2^{p^n}+1 \ = \ (2^{p^{n+1}}-1)/(2^{p^n}-1)</math> where p is the prime of apparition rank r (r(2)=1, r(3)=2, r(5)=3, ...) and n is greater or equa
    5 KB (726 words) - 09:57, 12 September 2021
  • PrimeGrid
    '''PrimeGrid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open I :[[PrimeGrid 321 Prime Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}.
    3 KB (458 words) - 10:28, 26 March 2024
  • Worktype
    ...omplished, in order to achieve the main goals of GIMPS (finding [[Mersenne prime]]s, ensuring that no Mersenne primes have been missed, and lastly finding [ ...The primality test. This is the only work type that can prove a number is prime.
    4 KB (603 words) - 02:31, 18 August 2019
  • Why participate in GIMPS?
    ...s of the form 2<sup>p</sup>-1, for some prime ''p'' (now called [[Mersenne prime|Mersennes]]). So the quest for these jewels began near 300 BC. ...studied (in chronological order) by Cataldi, Descartes, [[Pierre de Fermat|Fermat]], [[Marin Mersenne|Mersenne]], Frenicle, Leibniz, [[Leonhard Euler|Euler]]
    7 KB (1,252 words) - 09:47, 7 March 2019
  • Sieving program
    ...ng [[twin prime]]s of the same form) http://sites.google.com/site/kenscode/prime-programs *[[AthGFNSieve]] (performing sieving of generalized Fermat numbers b<sup>2<sup>n</sup></sup>+1) http://www.underbakke.com/AthGFNsv/
    2 KB (220 words) - 11:42, 7 March 2019
  • Introductory stuff
    It is feasible, but unlikely. A [[positive claim]], that of a new [[Mersenne prime]], is subject to [[Double check|double]] and [[triple check]]s by others, i ==What is a Mersenne prime?==
    14 KB (2,370 words) - 15:15, 17 August 2019
  • Glossary
    *'''[[Composite number]]''' - An [[integer]] that is not [[prime]]. *'''[[Fermat number]]''' - Numbers of the form <math>2^{2^n} + 1</math>.
    1 KB (190 words) - 10:55, 7 March 2019
  • Proth number
    A [[Proth prime]] is a Proth number, which is prime. [[Cullen number]]s ({{Kbn|+|n|2|n}}) and [[Fermat number]]s ({{Kbn|+|2<sup>n</sup>}}) are special forms of Proth numbers.
    670 bytes (104 words) - 10:59, 9 July 2021
  • Editing
    *The Prime Database: <code><nowiki>[https://primes.utm.edu/primes/status.php Status]</ ...re de Fermat|Fermat]]</nowiki></code> creates [[Wikipedia:Pierre de Fermat|Fermat]]
    5 KB (805 words) - 06:50, 1 May 2019
  • Mtsieve
    *cksieve: search for factors of [[Carol-Kynea prime]]s ...of {{Kbn|+|k|n}}, remaining terms are potential divisors of [[Generalized Fermat number]]s
    2 KB (338 words) - 06:58, 28 March 2023
  • Proth prime 2 1
    {{Proth prime |PRemarks=These n-values form the [[Fermat number|Fermat primes]].
    212 bytes (30 words) - 15:35, 2 October 2022
  • Proth prime 2 5
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    1 KB (144 words) - 11:12, 24 August 2021
  • Proth prime 2 7
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (267 words) - 21:47, 5 July 2023
  • Proth prime 2 9
    {{Proth prime For all even {{Vn}}-values {{Kbn|+|9|2|n}} is a [[Generalized Fermat number]].<br>
    3 KB (456 words) - 04:11, 15 May 2024
  • Proth prime 2 11
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (240 words) - 08:58, 11 January 2023
  • Proth prime 2 13
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    1 KB (175 words) - 07:07, 25 August 2021
  • Proth prime 2 15
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    3 KB (390 words) - 10:00, 25 August 2021
  • Proth prime 2 17
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    1 KB (149 words) - 04:18, 15 May 2024
  • Proth prime 2 19
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    1 KB (153 words) - 04:17, 15 May 2024
  • Cullen prime 2
    {{Cullen prime |CuReserved=PrimeGrid Cullen Prime Search
    2 KB (175 words) - 14:54, 19 September 2021
  • Williams prime MP 362
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|361|362|n}} is a [[Generalized Fermat number]].
    294 bytes (35 words) - 09:13, 1 August 2021
  • Williams prime MP 10
    {{Williams prime ...Kamada]<br>For all even {{Vn}}-values {{Kbn|+|9|10|n}} is a [[Generalized Fermat number]].
    1 KB (131 words) - 07:33, 23 April 2024
  • Williams prime MP 17
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|16|17|n}} is a [[Generalized Fermat number]].
    397 bytes (41 words) - 08:25, 1 August 2021
  • Proth prime 2 31
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    913 bytes (102 words) - 03:04, 15 May 2024
  • Proth prime 2 33
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (210 words) - 02:44, 15 May 2024
  • Proth prime small bases least n
    Here are shown the least ''n'' ≥ 1 generating a [[Proth prime]] of the form {{Kbn|+|k|b|n}} for 2 ≤ ''b'' ≤ 1030 and 2 ≤ ''k'' ≤ The data file can be found [[:File:Proth prime small bases least n.csv|here]].
    7 KB (795 words) - 08:03, 5 May 2024
  • Williams prime MP 37
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|36|37|n}} is a [[Generalized Fermat number]].
    350 bytes (36 words) - 08:36, 1 August 2021
  • Williams prime MP 50
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|49|50|n}} is a [[Generalized Fermat number]].
    292 bytes (31 words) - 08:42, 1 August 2021
  • Proth.exe
    * {{Kbn|+|1|k|n}} ([[Generalized Fermat number]]s) * {{Kbn|±|n|b|n}} ([[Cullen prime|Generalized Cullen]]/[[Woodall prime|Generalized Woodall]] numbers)
    667 bytes (101 words) - 16:44, 31 August 2021
  • Williams prime MP 122
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|121|122|n}} is a [[Generalized Fermat number]].
    276 bytes (33 words) - 08:48, 1 August 2021
  • Williams prime MP 257
    {{Williams prime |WiRemarks=For all even {{Vn}}-values {{Kbn|+|256|257|n}} is a [[Generalized Fermat number]].
    276 bytes (33 words) - 08:52, 1 August 2021
  • Proth prime 2 19683
    {{Proth prime {{HistC|2019-10-08|300000-4000000|PrimeGrid Fermat Divisor Search|P#8778#133619}}
    681 bytes (56 words) - 15:43, 11 July 2021
  • Template prototypes
    ==Template "Riesel prime" [[Riesel new|New]]== *[[:Template:Riesel prime]]{{#dpl:title=Template:Riesel prime|include=#Prototype}}
    1 KB (141 words) - 19:47, 15 March 2024
  • Statistics
    ...mber || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Mersenne prime|pages|R}}-2}}}} ...| base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Riesel prime|subcats|R}}-3}}}}
    11 KB (1,385 words) - 17:23, 5 April 2024
  • ToDo
    ...e:DGF|Template:DGF]]: displays only 19 entries, error if more, see [[Proth prime 3]] *expand more prime templates like Riesel prime template
    790 bytes (110 words) - 09:54, 9 October 2020
  • PrimeGrid Fermat Divisor Search
    ...le">[https://www.primegrid.com/forum_thread.php?id=8778&nowrap=true#149792 Fermat Divisor Search, Message 149792 - PrimeGrid Forums]</ref> The project searched for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}}, for the following ranges:<ref name=
    4 KB (448 words) - 09:13, 7 September 2021
  • Proth prime 3 16
    {{Proth prime 4;C:Generalized Fermat
    692 bytes (67 words) - 08:39, 12 July 2021
  • Proth prime 3 4
    {{Proth prime ...A005537}}<br>For all even {{Vn}}-values {{Kbn|+|4|3|n}} is a [[Generalized Fermat number]].
    1 KB (120 words) - 21:11, 1 August 2021
  • Proth prime 2 3125
    {{Proth prime {{HistC|2019-09-24|3322000|PrimeGrid Fermat Divisor Search|P#8778#133200}}
    677 bytes (57 words) - 08:55, 18 September 2021
  • Proth prime 2 35
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (236 words) - 02:10, 15 May 2024
  • Proth prime 2 121
    {{Proth prime |PRemarks=All values are [[Generalized Fermat number]]s.
    1 KB (120 words) - 01:43, 15 May 2024
  • Proth prime 2 21
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (275 words) - 04:14, 15 May 2024
  • Proth prime 2 23
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    940 bytes (120 words) - 04:12, 15 May 2024
  • Proth prime 2 25
    {{Proth prime |PRemarks=For all even {{Vn}}-values {{Kbn|+|25|2|n}} is a [[Generalized Fermat number]].
    2 KB (309 words) - 04:07, 15 May 2024
  • Proth prime 2 27
    {{Proth prime {{HistC|2024-04-30|5000000|PrimeGrid Proth Prime Search}}, effectively a double-check
    2 KB (321 words) - 03:46, 15 May 2024
  • Proth prime 2 29
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (277 words) - 03:09, 15 May 2024
  • Fermat divisor
    A <b>Fermat divisor</b> is a divisor of a [[Generalized Fermat number]] (in short a "GF Divisor"). ...number]] {{V|F<sub>n</sub>}} is of the form {{Kbn|+|k|n+2}} (so a [[Proth prime]]).
    445 bytes (71 words) - 09:09, 7 September 2021
  • Proth prime 2 289
    {{Proth prime ...[Generalized Fermat number#Special conditions for Proth primes|Generalized Fermat primes]].
    1 KB (153 words) - 09:56, 14 May 2024
  • Proth prime 2 37
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (259 words) - 02:40, 15 May 2024
  • Proth prime 2 39
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    4 KB (518 words) - 02:03, 15 May 2024
  • Proth prime 2 41
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    1,017 bytes (121 words) - 02:00, 15 May 2024
  • Proth prime 2 43
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (188 words) - 01:57, 15 May 2024
  • Proth prime 2 45
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    3 KB (389 words) - 01:56, 15 May 2024
  • Proth prime 2 47
    {{Proth prime {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    340 bytes (38 words) - 01:54, 15 May 2024
  • Proth prime 2 49
    {{Proth prime |PRemarks=For all {{Vn}}-values {{Kbn|+|49|2|n}} is a [[Generalized Fermat number]].
    1 KB (152 words) - 01:53, 15 May 2024
  • Proth prime 5 4
    {{Proth prime ...OEIS|l|A204322}}. See also {{NWi|MP|5|n}} <br>All primes are [[Generalized Fermat number]]s
    718 bytes (75 words) - 07:17, 14 February 2023
  • Robert Gerbicz
    ...iesel]], and (in an extended form) [[Generalized Fermat number|Generalized Fermat]] primality tests.
    607 bytes (78 words) - 20:45, 8 May 2023
  • Using LLR2 with PRPNet
    ...R2]] fork in place of [[Jean Penné]]'s [[LLR]] to perform Fermat probable prime tests with [[Gerbicz error checking]] with the [[PRPNet]] client. *PRPNet will use LLR2 to perform Fermat probable prime tests with [[Gerbicz error checking]].
    1 KB (207 words) - 16:14, 26 June 2023
  • PrimeGrid Generalized Fermat Prime Search
    ...t is searching for [[Generalized Fermat number#Dubner|Generalized Fermat]] prime numbers. ...hat 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 proje
    2 KB (310 words) - 06:38, 29 December 2023
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