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• Examples
  *[https://www.rieselprime.de/default.htm Riesel and Proth Prime Databse RPPDb] The <b>[[:Category:Carol-Kynea_prime|category]]</b> for Carol/Kynea primes holds example pages for some bases.
  11 KB (1,236 words) - 14:41, 3 September 2020
• Fermat number
  ...ber, and such primes are called '''Fermat primes'''. The only known Fermat primes are {{V|F}}₀,...,{{V|F}}₄. ...he sequence {{{V|p}}_{{Vn}}} is an infinite sequence of distinct primes.
  12 KB (1,913 words) - 14:35, 9 August 2021
• Sierpiński problem
  In early 2002, primes had been found for all but seventeen choices of {{Vk}}. At that point, the ...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
• Paul Seelhoff
  :28 [[Proth prime]]s for 3 &le; {{Vk}} &le; 97 :Found factor [[Proth prime 2 5|{{Kbn|+|5|2|39}}]] of {{DGF|36}}
  2 KB (195 words) - 00:13, 15 January 2024
• Riesel and Proth Prime Database
  ...nd Proth Prime Database''' is a database mainly of [[Riesel prime]]s and [[Proth prime]]s and some others subjects like [[Aliquot sequence]]s or [[Home prim *[https://www.rieselprime.de/default.htm Riesel and Proth Prime Database main page]
  380 bytes (59 words) - 14:14, 24 January 2019
• Primality test
  *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2<sup>{{Vn
  3 KB (501 words) - 05:20, 3 August 2021
• PSearch
  ...mputing project|distributed computing project]] in search of the largest [[Proth prime]]s. | At this date, it was the 15th largest prime number, and the 2nd largest Proth prime number.
  1 KB (182 words) - 08:17, 12 July 2020
• Generalized Fermat number
  In 1985, Dubner for the first time built a list of large primes of the form: b^{2^m}+1, ''b &ge; 2'' and ''m &ge; 1''. ...p.'' 67 (1998), pp. 441-446</ref> for the first time built a list of large primes of the form: a^{2^m}+b^{2^m}, ''b > a &
  5 KB (726 words) - 09:57, 12 September 2021
• PrimeGrid
  *Type Proth: :[[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
• Sieving program
  *[[FermFact]] (performing sieving of Proth numbers) http://www.fermatsearch.org/FermFact-09b.zip ...f numbers of the form k&times;2ⁿ+/-1) http://www.underbakke.com/primes/
  2 KB (220 words) - 11:42, 7 March 2019
• Proth prime
  ...e form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are often called Proth primes. *[[Proth's theorem]]
  656 bytes (91 words) - 07:02, 31 August 2020
• Riesel prime
  Although there's no official definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2^{{Vn}} > {{Vk}} are called like th *[https://www.mersenneforum.org/showthread.php?t=13180 "Post Top-5000 Primes Here"]: [https://www.mersenneforum.org/showpost.php?p=208696 #1 (2010-03-17
  2 KB (279 words) - 03:48, 24 April 2024
• 15k Search
  :In order to do this we use the fastest programs possible to return primes of special forms. ...nes, written by Paul Jobling, novice users will be more likely to look for primes, and will find them quicker.
  3 KB (517 words) - 14:51, 15 February 2019
• 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 table
  Automatically generated table from available [[:Category:Proth prime|Proth primes]]. ==Primes table==
  750 bytes (108 words) - 14:39, 12 July 2021
• Proth prime small bases least n
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|b|n}}, least ''n''-values}} 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'
  7 KB (795 words) - 08:03, 5 May 2024
• PrimeGrid Sierpiński base 5
  Finding primes for the [[Sierpiński number base 5]] problem. |include={Proth prime}:Pk,{Proth prime}:Pk
  2 KB (245 words) - 11:43, 5 September 2021
• Liskovets-Gallot conjectures
  ...ontinuing the [[CRUS Liskovets-Gallot]] subproject to find the remaining 9 primes required to prove the other 3 conjectures. [[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
• CRUS Liskovets-Gallot
  ...|Riesel]] and [[Proth prime|Proth]] {{Vk}}-values, divisible by 3, with no primes for {{Vn}}-values of a given parity. ...roven by [[Yves Gallot]], who provided examples for all four cases (Riesel/Proth, even/odd). Gallot further conjectured that these four examples are the sma
  7 KB (957 words) - 22:40, 10 June 2023
• Statistics
  | [[:Category:Mersenne prime|Mersenne primes]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Me | [[:Category:Riesel 2|Riesel primes {{Kbn|k|2|n}}]] || {{Vk}}-value || style="text-align:right;"|{{Num|{{PAGESI
  11 KB (1,385 words) - 17:23, 5 April 2024
• PrimeGrid Prime Sierpiński Problem
  ...], [[Proth prime 2 222113|222113]], [[Proth prime 2 225931|225931]], and [[Proth prime 2 237019|237019]]. The search is at {{Vn}} > {{Num|{{Multi Reservatio ...are also no known primes for {{Vk}} = [[Proth prime 2 22699|22699]] and [[Proth prime 2 67607|67607]], but these are already part of the standard Sierpińs
  2 KB (254 words) - 11:43, 5 September 2021
• PrimeGrid Cullen Prime Search
  ...[Proth prime 6679881|{{Kbn|+|6679881|2|6679881}}]] ([http://primes.utm.edu/primes/page.php?id=89536 2,010,852 digits]) ...[Proth prime 6328548|{{Kbn|+|6328548|2|6328548}}]] ([http://primes.utm.edu/primes/page.php?id=87775 1,905,090 digits])
  753 bytes (97 words) - 08:45, 12 September 2021
• Proth 2 3k-value
  {{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
• ToDo
  ...emplate:DGF|Template:DGF]]: displays only 19 entries, error if more, see [[Proth prime 3]] *list/table of Twin/SG primes with index
  790 bytes (110 words) - 09:54, 9 October 2020
• PrimeGrid Fermat Divisor Search
  ...mat divisors.<ref>[https://www.primegrid.com/forum_thread.php?id=8783 What primes can be Fermat divisors? - PrimeGrid Forums]</ref> ==Found primes==
  4 KB (448 words) - 09:13, 7 September 2021
• Florian Baur
  ...ently working on primes of the form {{NPr|1281979|n}}: {{Vn}} < {{Num|{{GP|Proth prime 2 1281979|PMaxn}}}} completed.
  271 bytes (34 words) - 15:09, 22 December 2023
• Proth 2 15k-value
  {{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
• Proth 2 2145k-value
  {{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
• Proth 2 2805k-value
  {{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
• Proth 2 1-300
  {{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
• Proth 2 Sierpinski
  category=Proth 2 Sierpinski include={Proth prime}:Pk,{Proth prime}:PRemarks
  741 bytes (99 words) - 21:18, 17 December 2023
• Proth 2 Count-0
  {{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
• Proth 2 Count-100
  {{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
• Proth 2 Missing-range
  {{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
• Proth 2 300-2000
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 300 < {{Vk}} < 2000}} ...atically generated table from available [[:Category:Proth 2 300-2000|Proth primes 300 < {{Vk}} < 2000]].
  873 bytes (117 words) - 08:15, 26 July 2021
• Proth 2 2000-4000
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 2000 < {{Vk}} < 4000}} ...tically generated table from available [[:Category:Proth 2 2000-4000|Proth primes 2000 < {{Vk}} < 4000]].
  878 bytes (117 words) - 08:17, 26 July 2021
• Proth 2 4000-6000
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 4000 < {{Vk}} < 6000}} ...tically generated table from available [[:Category:Proth 2 4000-6000|Proth primes 4000 < {{Vk}} < 6000]].
  887 bytes (118 words) - 08:18, 26 July 2021
• Proth 2 6000-8000
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 6000 < {{Vk}} < 8000}} ...tically generated table from available [[:Category:Proth 2 6000-8000|Proth primes 6000 < {{Vk}} < 8000]].
  887 bytes (118 words) - 08:20, 26 July 2021
• Proth 2 8000-10000
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 8000 < {{Vk}} < 10000}} ...ically generated table from available [[:Category:Proth 2 8000-10000|Proth primes 8000 < {{Vk}} < 10000]].
  883 bytes (117 words) - 08:21, 26 July 2021
• Proth 2 10e4-10e5
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Num|10000}} &le; {{Vk}} &le; {{Num|100000}}}} ...tically generated table from available [[:Category:Proth 2 10e4-10e5|Proth primes {{Num|10000}} < {{Vk}} < {{Num|100000}}]].
  1 KB (170 words) - 08:26, 26 July 2021
• Proth 2 10e5-10e6
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10⁵ < {{Vk}} < 10⁶}} ...tically generated table from available [[:Category:Proth 2 10e5-10e6|Proth primes 10⁵ < {{Vk}} < 10⁶]].
  1 KB (153 words) - 08:29, 26 July 2021
• Proth 2 10e6-10e7
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10⁶ < {{Vk}} < 10⁷}} ...tically generated table from available [[:Category:Proth 2 10e6-10e7|Proth primes 10⁶ < {{Vk}} < 10⁷]].
  1 KB (153 words) - 08:33, 26 July 2021
• Proth 2 10e7-10e8
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10⁷ < {{Vk}} < 10⁸}} ...tically generated table from available [[:Category:Proth 2 10e7-10e8|Proth primes 10⁷ < {{Vk}} < 10⁸]].
  1 KB (153 words) - 08:34, 26 July 2021
• Proth 2 10e8-10e9
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|k|n}}, 10⁸ < {{Vk}} < 10⁹}} ...tically generated table from available [[:Category:Proth 2 10e8-10e9|Proth primes 10⁸ < {{Vk}} < 10⁹]].
  1 KB (153 words) - 08:35, 26 July 2021
• Proth 2 10e9-10e10
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10⁹ < {{Vk}} < 10¹⁰}} ...ically generated table from available [[:Category:Proth 2 10e9-10e10|Proth primes 10⁹ < {{Vk}} < 10¹⁰]].
  1 KB (153 words) - 08:36, 26 July 2021
• Proth 2 10e10-infinity
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Vk}} > 10¹⁰}} ...ly generated table from available [[:Category:Proth 2 10e10-infinity|Proth primes {{Vk}} > 10¹⁰]].
  1 KB (146 words) - 08:38, 26 July 2021
• PrimeGrid 27121 Prime Search
  Searching for primes of the forms {{Kbn|±|27|n}} and {{Kbn|±|121|n}}. *[[Proth prime 2 27]]
  949 bytes (108 words) - 13:34, 5 November 2023
• Proth 3
  ==Primes table== |category=Proth 3
  405 bytes (56 words) - 22:02, 1 August 2021
• Proth 2 Low-weight
  {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with Nash weight < 1000}} Proth numbers {{Kbn|+|k|n}} where the [[Nash weight]] is smaller than 1000.
  944 bytes (121 words) - 18:22, 5 August 2021
• PrimeGrid Proth Prime Search
  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
• PrimeGrid Proth Prime Search Extended
  Finding primes for the form {{Kbn|+|k|n}} for 1200 < {{Vk}} < 10000 to {{Vn}}=3322000. [[Category:PrimeGrid Proth Prime Search Extended| ]]
  490 bytes (61 words) - 11:42, 5 September 2021
• PrimeGrid Proth Mega Prime Search
  Finding primes for the form {{Kbn|+|k|n}} for 1200 < {{Vk}} < 10000 to {{Vn}}=3600000. [[Category:PrimeGrid Proth Mega Prime Search| ]]
  862 bytes (109 words) - 09:55, 21 October 2023
• Proth prime 2 289
  {{Proth prime ...lized Fermat number#Special conditions for Proth primes|Generalized Fermat primes]].
  1 KB (127 words) - 10:01, 21 September 2021
• Proth prime 5 4
  {{Proth prime |PRemarks=The {{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