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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

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