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  • ...1}{p_i} = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \dotsb = \infty</math></pre> ...1}{p_i} = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \dotsb = \infty</math>
    11 KB (1,236 words) - 14:41, 3 September 2020
  • ...ese factorisations can be found at [http://www.prothsearch.com/fermat.html Prime Factors of Fermat Numbers] ...</sup> + 1 &equiv; 0 (mod 2<sup>{{V|a}}</sup> + 1).) In other words, every prime of the form {{Kbn|+|n}} is a Fermat number, and such primes are called '''F
    12 KB (1,913 words) - 14:35, 9 August 2021
  • {{Proth prime 11
    432 bytes (32 words) - 13:38, 2 January 2023
  • {{Proth prime {{HistC|2022-12-11|660000|(Alex_soldier)}}
    334 bytes (32 words) - 15:12, 27 January 2023
  • *{{Kbn|+|78557|12n+11}} is multiple of 13. |0||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24||25||26||27||28||29||30
    5 KB (650 words) - 10:25, 26 March 2024
  • |latest=4.0.5<br/><small>2023-11-11</small> It is written by [[Jean Penné]] and uses a recent release (30.11) of [[George Woltman]]'s [[gwnum]] library, to do fast multiplications and
    2 KB (300 words) - 22:00, 16 December 2023
  • ...g project|distributed computing project]] in search of the largest [[Proth prime]]s. | New prime
    1 KB (182 words) - 08:17, 12 July 2020
  • ...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 #If number <math>\sum_{i=0}^{p-1}\ (2^i)^{m} \ </math> is prime, then <math>m=p^n</math>.
    5 KB (726 words) - 09:57, 12 September 2021
  • Although there's no official definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk ...1-4199"]: [https://www.mersenneforum.org/showpost.php?p=425962 #1 (2016-02-11)] - [https://www.mersenneforum.org/showpost.php?p=541048 #7 (2020-03-27)]
    2 KB (279 words) - 03:48, 24 April 2024
  • {{Proth prime {{HistF|2020-10-25|16408818|James Scott Brown,PrimeGrid 321 Prime Search|561613}} ([https://www.primegrid.com/download/321-16408818.pdf Offic
    3 KB (336 words) - 16:58, 15 April 2024
  • {{Proth prime {{HistF|2012-11-10|5775996|Martyn Elvy,PrimeGrid Proth Prime Search}} ([http://www.primegrid.com/download/PPS-5775996.pdf Official annou
    2 KB (267 words) - 21:47, 5 July 2023
  • {{Proth prime 11;T:G
    3 KB (432 words) - 18:48, 9 April 2023
  • {{Proth prime |Pk=11
    2 KB (240 words) - 08:58, 11 January 2023
  • {{Proth prime {{HistF|2005-11-14|1861732|Peter Grobstich}}
    1 KB (175 words) - 07:07, 25 August 2021
  • {{Proth prime {{HistF|2012-11-25|2785940|Serge Batalov}}
    3 KB (390 words) - 10:00, 25 August 2021
  • {{Proth prime {{HistF|2005-02-11|853546|Joseph Bohanon}}
    1 KB (145 words) - 09:32, 26 August 2021
  • {{Proth prime 11
    371 bytes (31 words) - 08:06, 18 September 2021
  • {{Proth prime {{HistF|2013-03-18|1777488|Matt Jurach,PrimeGrid Proth Prime Search}}
    328 bytes (32 words) - 13:00, 12 August 2021
  • {{Proth prime {{HistF|2014-06-11|3570132|Fabrice Le Foulher,PrimeGrid Proth Mega Prime Search}} ([https://www.primegrid.com/download/mega-3570132.pdf Official ann
    2 KB (202 words) - 11:31, 31 August 2021
  • {{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
  • {{Proth prime {{HistF|2013-05-18|2898957|Mark Molder,PrimeGrid Proth Prime Search}}
    2 KB (279 words) - 19:01, 9 April 2023
  • {{Proth prime {{HistF|2013-03-20|1817862|Luis Resto,PrimeGrid Proth Prime Search}}
    1 KB (103 words) - 09:49, 29 September 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|2019-07-18|2772512|Daniel Thonon,PrimeGrid Proth Prime Search}}
    3 KB (289 words) - 10:52, 21 September 2021
  • {{Proth prime {{HistF|2022-03-24|3218214|Florian Baur,PrimeGrid Proth Prime Search}}
    2 KB (186 words) - 18:58, 9 April 2023
  • {{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|1998-11-21|15943|David Hanson}}
    1 KB (124 words) - 08:43, 12 July 2021
  • {{Proth prime {{HistF|1998-11-08|18880|Chris Caldwell}}
    631 bytes (65 words) - 08:21, 12 July 2021
  • |include={Proth prime}:Pk,{Proth prime}:Pk |secseparators=[[Proth prime 5 ,|,,]]
    2 KB (245 words) - 11:43, 5 September 2021
  • {{Proth prime ...y part of [[Multi Reservation:25|Multi Reservation 25]]: [[PrimeGrid Proth Prime Search Extended]].
    1 KB (161 words) - 09:08, 10 May 2024
  • ...]], which relate to the smallest [[Riesel prime|Riesel]] and [[Proth prime|Proth]] {{Vk}}-values, divisible by 3, with no primes for {{Vn}}-values of a give ...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
  • {{Proth prime 11
    459 bytes (40 words) - 09:57, 12 July 2021
  • ...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
  • {{Proth prime {{HistF|2020-09-11|1153674|Ryan Propper}}
    657 bytes (66 words) - 08:33, 12 July 2021
  • {{Proth prime 11
    877 bytes (71 words) - 00:12, 30 April 2024
  • {{Proth prime |PDate=2020-10-11
    358 bytes (25 words) - 15:43, 11 July 2021
  • {{Proth prime |PDate=2020-11-25
    225 bytes (24 words) - 14:34, 7 April 2023
  • {{Proth prime 11
    871 bytes (98 words) - 12:55, 8 April 2023
  • {{Proth prime |PDate=2020-11-25
    225 bytes (24 words) - 14:35, 7 April 2023
  • {{Proth prime 11
    859 bytes (98 words) - 13:02, 8 April 2023
  • *2021-03-01: [[Proth prime 2 25|{{Kbn|+|25|8788628}}]] *2021-02-17: [[Proth prime 2 17|{{Kbn|+|17|8636199}}]]
    4 KB (448 words) - 09:13, 7 September 2021
  • {{Proth prime 11
    642 bytes (53 words) - 09:32, 12 July 2021
  • {{Williams prime |WiMaxn={{Reuse Primelist|Proth prime 11 120|PMaxn|2}}
    272 bytes (36 words) - 08:47, 1 August 2021
  • {{Proth prime |Pb=11
    313 bytes (27 words) - 09:51, 12 July 2021
  • {{Proth prime |PDate=2020-11-13
    288 bytes (26 words) - 10:19, 12 July 2021
  • {{Proth prime |PDate=2020-11-15
    391 bytes (32 words) - 10:04, 12 July 2021
  • {{Proth prime {{HistC|2021-11-22|5250000|Florian Baur|593617}}
    913 bytes (83 words) - 17:01, 12 January 2024
  • {{Proth prime {{HistF|2004-03-11|108875|Peter Benson}}
    402 bytes (38 words) - 09:36, 12 July 2021
  • {{Proth prime 11
    358 bytes (33 words) - 08:59, 12 July 2021
  • {{Proth prime {{HistF|2019-11-28|1154598|Matthias Baur}}
    1 KB (120 words) - 21:11, 1 August 2021
  • {{Proth prime {{HistF|2019-09-11|2867399|Ricky L Hubbard,PrimeGrid}}
    677 bytes (57 words) - 08:55, 18 September 2021
  • {{Proth prime {{HistF|2014-07-05|3587843|Peter Tibbott,PrimeGrid Proth Mega Prime Search}} ([https://www.primegrid.com/download/mega-3587843.pdf Official ann
    2 KB (228 words) - 10:04, 1 September 2021
  • {{Proth prime {{HistC|2021-04-08|10000000|PrimeGrid 27121 Prime Search|P#9612#149921}}
    1 KB (112 words) - 19:02, 9 April 2023
  • {{Proth prime {{HistF|2004-11-04|1830919|Curtis Cooper}}
    2 KB (267 words) - 10:18, 26 August 2021
  • {{Proth prime {{HistF|2019-10-11|4300741|Nicholas Mohacsy,PrimeGrid Fermat Divisor Search}}
    872 bytes (112 words) - 09:54, 1 September 2021
  • {{Proth prime {{HistF|2013-04-22|2927222|Rick Channing,PrimeGrid Proth Prime Search}}
    2 KB (301 words) - 00:37, 9 March 2023
  • {{Proth prime {{HistR|2023|PrimeGrid Proth Prime Search}}
    2 KB (306 words) - 09:11, 12 April 2023
  • {{Proth prime 11;T:G
    2 KB (269 words) - 15:14, 30 August 2021
  • {{Proth prime 11
    1 KB (91 words) - 14:49, 9 May 2024
  • {{Proth prime {{HistF|2021-08-03|3374198|Daniel Zuyuan Lu,PrimeGrid Proth Mega Prime Search}}
    1 KB (95 words) - 08:37, 11 August 2021
  • {{Proth prime {{HistF|2021-08-03|3374939|Mike McDonald,PrimeGrid Proth Mega Prime Search}}
    1 KB (89 words) - 09:34, 11 August 2021
  • {{Proth prime {{HistF|2021-07-25|3373383|Jens Riemann,PrimeGrid Proth Mega Prime Search}}
    657 bytes (57 words) - 15:05, 9 May 2024
  • {{Proth prime {{HistF|2021-07-23|3373135|Vadim Bulanov,PrimeGrid Proth Mega Prime Search}}
    769 bytes (66 words) - 14:33, 9 May 2024
  • {{Proth prime {{HistF|2021-07-22|3069884|Toshiya Satoh,PrimeGrid Proth Prime Search}}
    1 KB (123 words) - 15:54, 15 August 2021
  • {{Proth prime 3;C:Is {{DGF|2|11}}
    2 KB (152 words) - 10:56, 17 September 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|2021-05-21|3015314|Stefan Larsson,PrimeGrid Proth Prime Search}}
    1 KB (99 words) - 12:32, 5 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|2021-07-02|3063847|Lee Blyth,PrimeGrid Proth Prime Search}}
    2 KB (154 words) - 04:54, 21 September 2021
  • {{Proth prime 11
    954 bytes (92 words) - 09:38, 6 September 2021
  • {{Proth prime {{HistF|2021-05-01|3019445|Krzysztof Ostaszewski,PrimeGrid Proth Prime Search}}
    2 KB (186 words) - 10:09, 6 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 11
    3 KB (304 words) - 19:58, 13 September 2021
  • {{Proth prime 11
    2 KB (223 words) - 07:20, 15 September 2021
  • {{Proth prime 11
    3 KB (333 words) - 10:22, 15 September 2021
  • {{Proth prime {{HistF|2018-03-28|3501974|Stefan Larsson,PrimeGrid Proth Mega Prime Search}}
    1,003 bytes (89 words) - 12:36, 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|2021-05-18|3037988|Stefan Larsson,PrimeGrid Proth Prime Search}}
    1 KB (102 words) - 06:42, 20 September 2021
  • {{Proth prime 11
    3 KB (328 words) - 15:00, 20 September 2021
  • {{Proth prime {{HistF|2021-06-11|3055695|Rudi Tapper,PrimeGrid Proth Prime Search}}
    1 KB (97 words) - 15:34, 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|2022-11-08|15474010|Ryan Propper}}
    2 KB (251 words) - 22:19, 5 July 2023
  • {{Proth prime 2;C:Is {{DGF|1|11|6}}
    4 KB (510 words) - 13:09, 27 September 2021
  • {{Proth prime 11
    2 KB (176 words) - 08:38, 28 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|2015-01-07|3411847|William Darney,PrimeGrid Proth Mega Prime Search}} ([http://www.primegrid.com/download/mega-3411847.pdf Official anno
    2 KB (236 words) - 09:07, 3 October 2021
  • {{Proth prime {{HistF|2021-07-16|3068511|Randall Scalise,PrimeGrid Proth Prime Search}}
    2 KB (245 words) - 09:34, 4 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|2021-09-13|3087428|Stefan Larsson,PrimeGrid Proth Prime Search}}
    912 bytes (84 words) - 12:14, 4 October 2021
  • {{Proth prime {{HistF|2021-09-13|3087514|Andreas H. Mahnken,PrimeGrid Proth Prime Search}}
    1 KB (129 words) - 12:31, 4 October 2021
  • {{Proth prime {{HistF|2021-09-13|3087543|Phil Deakin,PrimeGrid Proth Prime Search}}
    982 bytes (92 words) - 22:55, 5 July 2023
  • {{Proth prime {{HistF|2018-10-25|2670409|Randall Scalise,PrimeGrid Proth Prime Search}}
    1 KB (136 words) - 13:52, 4 October 2021
  • {{Proth prime 11;T:G
    949 bytes (113 words) - 04:40, 27 March 2023
  • {{Proth prime {{HistF|2020-11-12|7513661|Hiroyuki Okazaki,PrimeGrid Fermat Divisor Search}} ([http://www.
    3 KB (381 words) - 14:38, 5 October 2021
  • {{Proth prime {{HistF|2022-09-11|9187790|Ryan Propper}}
    1 KB (144 words) - 22:24, 5 July 2023
  • {{Proth prime {{HistF|2021-09-20|3091825|Stefan Larsson,PrimeGrid Proth Prime Search}}
    2 KB (215 words) - 13:02, 8 October 2021
  • {{Proth prime {{HistF|2021-09-26|3094582|Sascha Beat Dinkel,PrimeGrid Proth Prime Search}}
    437 bytes (47 words) - 13:30, 8 October 2021
  • {{Proth prime 11
    490 bytes (32 words) - 05:33, 11 October 2021
  • {{Proth prime {{HistC|2023-03-11|300000|(Alex_soldier)|626575}}, results included
    1 KB (126 words) - 18:51, 27 October 2023
  • {{Proth prime {{HistC|2020-04-11|300000|Daniel Zuyuan Lu|P#9107#139607}}
    701 bytes (80 words) - 19:38, 5 April 2023
  • {{Proth prime 11
    3 KB (312 words) - 00:17, 30 April 2024
  • {{Proth prime 11
    1 KB (75 words) - 11:17, 22 April 2024
  • {{Proth prime {{HistC|2017-11-02|1000000|(Alex_soldier)|638872}}, results included, released
    519 bytes (41 words) - 17:59, 22 September 2023
  • {{Proth prime {{HistF|2009-11-02|528030|Jun Tajima}}
    618 bytes (46 words) - 23:35, 22 September 2023
  • {{Proth prime {{HistF|2023-11-23|4379097|Dawid Kwiatkowski,PrimeGrid Proth Prime Search}}
    4 KB (438 words) - 11:22, 28 March 2024
  • *Type: Riesel,Proth,SG,Twin,GFN,... ...:center; background:#FF9900; font-size:120%; font-weight:bold;">NPLB Drive 11</div>
    3 KB (372 words) - 16:57, 11 May 2024