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  • ...ath>\sum_{i=1}^\infty \frac{1}{p_i} = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \dotsb = \infty</math></pre> :<math>\sum_{i=1}^\infty \frac{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
  • :{{V|F}}<sub>1</sub> = {{Kbn|+|2}} = 5 :{{V|F}}<sub>5</sub> = {{Kbn|+|32}} = 4294967297 = 641 &times; 6700417
    12 KB (1,913 words) - 14:35, 9 August 2021
  • *{{Kbn|+|78557|4n+1}} is multiple of 5. (those values form a [[covering set]] of {3, 5, 7, 13, 19, 37, 73}) we can prepare the following table for the exponents m
    5 KB (650 words) - 10:25, 26 March 2024
  • :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
  • ...: "The test that we today call Pépin's test is actually [[Proth's theorem|Proth's test]] with a proof provided by Lucas". ...ralized Fermat 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
  • ...^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 equal to 0. #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
  • '''PrimeGrid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open I *Type Proth:
    3 KB (458 words) - 10:28, 26 March 2024
  • {{Proth prime |PCount=5
    212 bytes (30 words) - 15:35, 2 October 2022
  • {{Proth prime 5;T:G
    3 KB (336 words) - 16:58, 15 April 2024
  • {{Proth prime |Pk=5
    1 KB (144 words) - 11:12, 24 August 2021
  • {{Proth prime 5;T:G
    2 KB (240 words) - 08:58, 11 January 2023
  • {{Williams prime |WiBase=5
    260 bytes (36 words) - 08:29, 11 February 2023
  • {{Williams prime |WiMaxn={{Reuse Primelist|Proth prime 6 5|PMaxn|1}}
    260 bytes (36 words) - 16:08, 10 February 2023
  • {{Williams prime |WiMaxn={{Reuse Primelist|Proth prime 5 24|PMaxn|2}}
    358 bytes (45 words) - 08:28, 1 August 2021
  • {{Williams prime |WiMaxn={{Reuse Primelist|Proth prime 2 31|PMaxn|5}}
    263 bytes (36 words) - 08:31, 1 August 2021
  • {{Williams prime |WiMaxn={{#expr:floor({{GP|Proth prime 2 33|PMaxn}}/5)}}
    377 bytes (47 words) - 11:53, 13 July 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 5
    2 KB (279 words) - 19:01, 9 April 2023
  • {{Proth prime 5
    2 KB (245 words) - 10:36, 12 September 2021
  • {{Proth prime 5;T:T
    2 KB (186 words) - 18:58, 9 April 2023
  • {{Proth prime 5
    2 KB (177 words) - 09:40, 7 September 2021
  • {{Proth prime 5;T:G
    1 KB (99 words) - 11:13, 17 September 2021
  • {{Proth prime 5
    1 KB (19 words) - 16:07, 11 July 2021
  • {{Proth prime 5
    681 bytes (56 words) - 15:43, 11 July 2021
  • {{Proth prime |Pb=5
    122 bytes (13 words) - 10:23, 12 July 2021
  • Finding primes for the [[Sierpiński number base 5]] problem. |category=PrimeGrid Sierpiński base 5
    2 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- got an irregular contribution of odd and even exponents yielding a prime.
    2 KB (367 words) - 12:42, 9 May 2024
  • {{Proth prime 5
    396 bytes (50 words) - 09:17, 10 May 2024
  • {{Proth prime 5
    403 bytes (36 words) - 09:59, 12 July 2021
  • {{Proth prime |Pb=5
    582 bytes (53 words) - 10:16, 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 |Pb=5
    314 bytes (35 words) - 08:43, 10 April 2023
  • {{Proth prime |Pb=5
    310 bytes (35 words) - 08:44, 10 April 2023
  • {{Proth prime |Pb=5
    122 bytes (13 words) - 10:27, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:28, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:32, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:33, 12 July 2021
  • {{Proth prime |Pb=5
    124 bytes (13 words) - 11:12, 12 July 2021
  • {{Proth prime |Pb=5
    124 bytes (13 words) - 11:12, 12 July 2021
  • {{Proth prime |Pb=5
    124 bytes (13 words) - 11:08, 12 July 2021
  • {{Proth prime |Pb=5
    124 bytes (13 words) - 11:06, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 11:05, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 11:04, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 11:04, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 11:03, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 11:01, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:57, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:56, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:56, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:55, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:54, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:54, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:46, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:44, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:42, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:41, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:40, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:39, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:38, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:36, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:36, 12 July 2021
  • {{Proth prime |Pb=5
    123 bytes (13 words) - 10:35, 12 July 2021
  • {{Proth prime |PRemarks=Covering set = [3, 5, 7, 13, 19, 37, 73]
    165 bytes (15 words) - 07:30, 26 July 2021
  • {{Proth prime |PRemarks=Covering set = [3, 5, 7, 13, 17, 241]
    159 bytes (15 words) - 07:33, 26 July 2021
  • {{Proth prime 5
    558 bytes (46 words) - 09:40, 12 July 2021
  • * 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions: *2021-03-01: [[Proth prime 2 25|{{Kbn|+|25|8788628}}]]
    4 KB (448 words) - 09:13, 7 September 2021
  • {{Proth prime 5
    642 bytes (53 words) - 09:32, 12 July 2021
  • {{Proth prime 5;C:Divides Phi(3^5,2)
    2 KB (204 words) - 11:06, 18 April 2023
  • {{Proth prime |Pb=5
    288 bytes (26 words) - 10:19, 12 July 2021
  • {{Proth prime 5
    1 KB (105 words) - 17:50, 16 August 2022
  • {{Proth prime 5
    489 bytes (38 words) - 08:11, 12 July 2021
  • {{Proth prime 5
    692 bytes (67 words) - 08:39, 12 July 2021
  • {{Proth prime 5
    370 bytes (26 words) - 08:40, 12 July 2021
  • {{Proth prime 5
    364 bytes (21 words) - 08:41, 12 July 2021
  • {{Proth prime 5
    473 bytes (37 words) - 18:11, 2 August 2021
  • {{Proth prime |Pb=5
    320 bytes (36 words) - 08:44, 10 April 2023
  • {{Proth prime 5;T:T
    1 KB (97 words) - 14:27, 9 May 2024
  • {{Proth prime 5;T:G
    2 KB (267 words) - 10:18, 26 August 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>5</sup> < {{Vk}} < 10<sup>6</sup>}} ...ted table from available [[:Category:Proth 2 10e5-10e6|Proth primes 10<sup>5</sup> < {{Vk}} < 10<sup>6</sup>]].
    1 KB (153 words) - 08:29, 26 July 2021
  • {{Proth prime 5;T:G
    2 KB (269 words) - 15:14, 30 August 2021
  • {{Proth prime 5
    769 bytes (66 words) - 14:33, 9 May 2024
  • {{Proth prime 5;T:T
    2 KB (157 words) - 09:38, 7 September 2021
  • {{Proth prime 5
    4 KB (409 words) - 09:41, 7 September 2021
  • {{Proth prime 5
    2 KB (154 words) - 04:54, 21 September 2021
  • {{Proth prime 5
    2 KB (186 words) - 10:09, 6 September 2021
  • {{Proth prime 5
    3 KB (304 words) - 19:58, 13 September 2021
  • {{Proth prime 5
    864 bytes (79 words) - 12:53, 15 September 2021
  • {{Proth prime 5
    3 KB (328 words) - 15:00, 20 September 2021
  • {{Proth prime 3;T:T;C:Is {{DGF|2|5|1}}
    4 KB (510 words) - 13:09, 27 September 2021
  • {{Proth prime 5
    2 KB (176 words) - 08:38, 28 September 2021
  • {{Proth prime 5
    2 KB (245 words) - 09:34, 4 October 2021
  • {{Proth prime 5
    403 bytes (44 words) - 19:12, 5 April 2023
  • {{Proth prime |Pk=5
    1 KB (126 words) - 18:51, 27 October 2023
  • {{Proth prime |Pb=5
    718 bytes (75 words) - 07:17, 14 February 2023
  • {{Proth prime 5
    3 KB (312 words) - 00:17, 30 April 2024
  • {{Proth prime 5
    1 KB (75 words) - 11:17, 22 April 2024
  • {{Proth prime 5;T:T
    4 KB (438 words) - 11:22, 28 March 2024
  • {{Proth prime 5
    326 bytes (16 words) - 15:46, 9 May 2024
  • *Type: Riesel,Proth,SG,Twin,GFN,... ...ng all 2001 &le; {{Vk}} &le; 2999 for 425001 &le; {{Vn}} &le; 600000 minus 5 {{Vk}}'s that are reserved and not fully processed for the area.
    3 KB (372 words) - 16:57, 11 May 2024