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Create the page "Proth k=1-300" on this wiki! See also the search results found.
- *'''[[Proth's theorem]]''' -- (1878) Let {{V|N}} = {{Kbn|+|k|2|m}} with odd {{Vk}} < 2<sup>{{V|m}}</sup>. If there is an integer {{V|a}} ...'s theorem is known as '''[[Pépin's test]]'''. Although Pépin's test and Proth's theorem have been implemented on computers to prove the compositeness of12 KB (1,913 words) - 14:35, 9 August 2021
- Consider numbers of the form {{V|N}} = {{Kbn|+|k|n}}, where {{Vk}} is odd and {{Vn}} > 0. If, for some fixed {{Vk}}, every i ...699]], [[Proth prime 2 24737|24737]], [[Proth prime 2 55459|55459]], and [[Proth prime 2 67607|67607]] (current status [https://www.primegrid.com/stats_sob_5 KB (650 words) - 10:25, 26 March 2024
- A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. *[[Riesel and Proth Prime Database]]827 bytes (112 words) - 08:21, 25 March 2024
- *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}}, making it useful in several [[distrib3 KB (501 words) - 05:20, 3 August 2021
- ...: "The test that we today call Pépin's test is actually [[Proth's theorem|Proth's test]] with a proof provided by Lucas". ...t number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3.2 KB (401 words) - 14:40, 6 March 2019
- **[[Lucas-Lehmer-Riesel algorithm]] for {{Kbn|k|n}} numbers. **[[Proth's theorem|Proth algorithm]] for {{Kbn|+|k|n}} numbers.2 KB (300 words) - 22:00, 16 December 2023
- ...F_{n,2}</math> numbers can be proven prime by using [[Pépin's test]] with k=5. ...[[Generalized Fermat number]]s for any [[Proth prime|Proth primes {{Kbn|+|k|n}}]] are listed as ''GF Divisor'' on their own page. They are listed as ''5 KB (726 words) - 09:57, 12 September 2021
- *Type Proth: ...rime Search|Proth Prime Search]]: searching for primes of the form {{Kbn|+|k|2|n}}.3 KB (458 words) - 10:28, 26 March 2024
- ...of numbers of the form K × 2<sup>n</sup> + 1 or - 1. Independent of K's, but good for many N's too) and [[TPSieve]] (similar to PPSieve, but for *[[FermFact]] (performing sieving of Proth numbers) http://www.fermatsearch.org/FermFact-09b.zip2 KB (220 words) - 11:42, 7 March 2019
- This article is about '''Proth's theorem'''. Proth's theorem (1878) states:549 bytes (88 words) - 18:15, 28 September 2023
- ...in the form {{Kbn|+|k|n}} with 2<sup>''n''</sup> > ''k'' are often called Proth primes. *[[Proth's theorem]]656 bytes (91 words) - 07:02, 31 August 2020
- ...ial definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}} are called like this on many pages. ...mersenneforum.org/showthread.php?t=29635 "Team drive #1 for {{Vk}}<300: 26 k's for {{Vn}}>2M"]: [https://www.mersenneforum.org/showpost.php?p=655608 #12 KB (279 words) - 03:48, 24 April 2024
- In [[number theory]], a '''Proth number''' is a number of the form :{{V|N}} = {{Kbn|+|k|2|n}}670 bytes (104 words) - 10:59, 9 July 2021
- It is also used by [[LLR]] and [[LLR2]] to ensure validity of [[Proth prime|Proth]] tests and PRP tests on base-2 [[Riesel prime]] candidates, and by those p ...the original formulation of the Gerbicz error check for [[Proth's theorem|Proth tests]], as described in [https://www.mersenneforum.org/showthread.php?t=223 KB (528 words) - 14:59, 3 October 2023
- {{Proth prime {{HistF|2012-01-29|1455620|Gus Obermeyer,PrimeGrid Proth Prime Search}}1 KB (103 words) - 12:07, 7 September 2021
- {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|b|n}}, least ''n''-values}} ...h prime]] of the form {{Kbn|+|k|b|n}} for 2 ≤ ''b'' ≤ 1030 and 2 ≤ ''k'' ≤ 12.7 KB (795 words) - 08:03, 5 May 2024
- |title=Proth '''Proth.exe''' is an ancient program that implements [[Proth's theorem]]. It is used to test the primality of the following forms:667 bytes (101 words) - 16:44, 31 August 2021
- {{Proth prime {{HistF|2015-02-14|2668448|Gerrit Slomma,PrimeGrid Proth Prime Search}}2 KB (245 words) - 10:36, 12 September 2021
- {{Proth prime {{HistF|2014-04-01|2135642|Joshua Whiteley,PrimeGrid Proth Prime Search}}2 KB (177 words) - 09:40, 7 September 2021
- {{Proth prime {{HistF|2021-05-16|3036045|Nathaniel Adam,PrimeGrid Proth Prime Search}}1 KB (99 words) - 11:13, 17 September 2021
- ==k-values left== |include={Proth prime}:Pk,{Proth prime}:Pk2 KB (245 words) - 11:43, 5 September 2021
- ...ding primes of the required parity for all smaller {{Vk}}-values. The even Proth conjecture was proven in 2015, and CRUS is continuing the [[CRUS Liskovets- [[Valery Liskovets]] studied the list of {{Kbn|+|k|n}} primes and observed, that the {{Vk}}'s ({{Vk}} divisible by 3)2 KB (367 words) - 12:42, 9 May 2024
- ...ris Nash]] gave a weight to show the number of remaining values of {{Kbn|+|k|n}} after sieving the range 100000 < {{Vn}} < 110000 after performing a Nas A later definition was also done for {{Kbn|k|n}}.2 KB (330 words) - 09:11, 23 September 2021
- | [[:Category:Riesel 2|Riesel primes {{Kbn|k|2|n}}]] || {{Vk}}-value || style="text-align:right;"|{{Num|{{PAGESINCATEGOR | [[:Category:Riesel prime|Riesel primes {{Kbn|k|b|n}}]], {{Vb}}>2 || base || style="text-align:right;"|{{Num|{{#expr:{{P11 KB (1,385 words) - 17:23, 5 April 2024
- To solve the [[Sierpiński problem]] by finding a prime of the form {{Kbn|+|k|n}} for each remaining value of {{Vk}} < 78,557. |include={Proth prime}:Pk,{Proth prime}:Pk1 KB (135 words) - 11:42, 5 September 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 3 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 3.1 KB (156 words) - 09:18, 23 July 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 15 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 15.1 KB (156 words) - 09:22, 23 July 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 2145 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 2145.1 KB (156 words) - 09:36, 23 July 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 2805 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 2805.1 KB (158 words) - 09:16, 22 March 2024
- {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Vk}} < 300}} Automatically generated table from available [[:Category:Proth 2 1-300|Proth primes {{Vk}} < 300]].850 bytes (117 words) - 17:18, 25 July 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with no prime value so far}} Proth numbers {{Kbn|+|k|n}} where no prime values are known.867 bytes (117 words) - 07:46, 26 July 2021
- {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with 100 and more primes}} Proth numbers {{Kbn|+|k|n}} with 100 or more prime values {{Vn}}.916 bytes (122 words) - 07:51, 26 July 2021
- {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}} with missing ranges}} Proth {{Vk}}-values with missing ranges below the largest known prime for that {{778 bytes (107 words) - 07:57, 26 July 2021
- Finding primes for the form {{Kbn|+|k|n}} for 100 < {{Vk}} < 1200 to {{Vn}}=3322000. [[Category:PrimeGrid Proth Prime Search| ]]468 bytes (59 words) - 07:11, 12 October 2021
- {{Proth prime {{HistF|2018-02-27|3487253|James Scott Brown,PrimeGrid Proth Mega Prime Search}}2 KB (157 words) - 09:38, 7 September 2021
- {{Proth prime {{HistF|2021-08-23|3078792|James Scott Brown,PrimeGrid Proth Prime Search}}4 KB (409 words) - 09:41, 7 September 2021
- {{Proth prime {{HistF|2021-05-02|3025527|Barry Schnur,PrimeGrid Proth Prime Search}}3 KB (248 words) - 11:22, 7 September 2021
- {{Proth prime ...rks=All primes are also [[Generalized Fermat number#Special conditions for Proth primes|Generalized Fermat primes]].1 KB (127 words) - 10:01, 21 September 2021
- {{Proth prime {{HistF|2021-07-10|3066009|Ryan Propper,PrimeGrid Proth Prime Search}}3 KB (304 words) - 19:58, 13 September 2021
- {{Proth prime {{HistF|2021-05-06|3029342|Stefan Larsson,PrimeGrid Proth Prime Search}}2 KB (223 words) - 07:20, 15 September 2021
- {{Proth prime {{HistF|2021-05-04|3027769|Sota Tajika,PrimeGrid Proth Prime Search}}3 KB (333 words) - 10:22, 15 September 2021
- {{Proth prime {{HistF|2021-05-17|3037565|Stefan Larsson,PrimeGrid Proth Prime Search}}723 bytes (77 words) - 06:27, 20 September 2021
- {{Proth prime {{HistF|2021-05-21|3040438|Brian D. Niegocki,PrimeGrid Proth Prime Search}}2 KB (224 words) - 09:04, 20 September 2021
- {{Proth prime {{HistF|2021-06-11|3056181|Brian D. Niegocki,PrimeGrid Proth Prime Search}}2 KB (167 words) - 07:41, 22 September 2021
- {{Proth prime {{HistF|2021-09-24|3094072|Adrian Schori,PrimeGrid Proth Prime Search}}3 KB (263 words) - 09:45, 28 September 2021
- {{Proth prime {{HistF|2020-11-12|2894566|Dale Laluk,PrimeGrid Proth Prime Search}}2 KB (204 words) - 07:56, 3 October 2021
- {{Proth prime {{HistF|2021-07-19|3069092|Sascha Beat Dinkel,PrimeGrid Proth Prime Search}}2 KB (157 words) - 10:53, 4 October 2021
- {{Proth prime {{HistF|2018-10-25|2670409|Randall Scalise,PrimeGrid Proth Prime Search}}1 KB (136 words) - 13:52, 4 October 2021
- {{Proth prime {{HistF|2023-11-23|4379097|Dawid Kwiatkowski,PrimeGrid Proth Prime Search}}4 KB (438 words) - 11:22, 28 March 2024
