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  • ...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 |PCount=9
    334 bytes (32 words) - 15:12, 27 January 2023
  • |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 ...e covered, meaning that no member of the sequence {{Kbn|+|78557|n}} can be prime. The same arguments can be said of the numbers 271129, 271577, 322523, 3277
    5 KB (650 words) - 10:25, 26 March 2024
  • ...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
  • {{Proth prime 1320487;9;T:G
    1 KB (144 words) - 11:12, 24 August 2021
  • {{Proth prime |Pk=9
    3 KB (456 words) - 04:11, 15 May 2024
  • {{Proth prime 9;T:G
    3 KB (412 words) - 08:00, 15 May 2024
  • {{Williams prime |WiBase=9
    387 bytes (53 words) - 08:30, 12 July 2021
  • {{Williams prime |WiMaxn={{#expr:floor({{GP|Proth prime 2 511|PMaxn}}/9)}}
    272 bytes (37 words) - 09:15, 1 August 2021
  • {{Williams prime |WiMaxn={{#expr:floor({{GP|Proth prime 2 9|PMaxn}}/3)}}
    278 bytes (38 words) - 11:59, 13 July 2021
  • {{Williams prime |WiBase=9
    268 bytes (37 words) - 08:34, 12 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 9;T:G
    3 KB (299 words) - 01:29, 15 May 2024
  • {{Proth prime 9
    3 KB (315 words) - 09:37, 14 May 2024
  • {{Proth prime 9
    2 KB (186 words) - 04:31, 14 May 2024
  • {{Williams prime |WiMaxn={{#expr:floor({{GP|Proth prime 2 513|PMaxn}}/9)}}
    272 bytes (37 words) - 12:05, 13 July 2021
  • {{Proth prime |PRemarks=See also {{NWi|MP|9|n}}<br>The {{OEIS|l|A005538}}
    631 bytes (65 words) - 08:21, 12 July 2021
  • {{Proth prime |PMultiRes=9
    122 bytes (13 words) - 10:23, 12 July 2021
  • {{Proth prime 9
    545 bytes (60 words) - 14:28, 7 April 2023
  • {{Proth prime 9
    318 bytes (34 words) - 15:42, 11 July 2021
  • *[[Multi Reservation:9|here]] |include={Proth prime}:Pk,{Proth prime}:Pk
    2 KB (245 words) - 11:43, 5 September 2021
  • ...continuing the [[CRUS Liskovets-Gallot]] subproject to find the remaining 9 primes required to prove the other 3 conjectures. got an irregular contribution of odd and even exponents yielding a prime.
    2 KB (367 words) - 12:42, 9 May 2024
  • {{Proth prime |PCount=9
    396 bytes (50 words) - 09:17, 10 May 2024
  • {{Proth prime 9
    657 bytes (66 words) - 08:33, 12 July 2021
  • {{Proth prime |PMultiRes=9
    122 bytes (13 words) - 10:27, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:28, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:32, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:33, 12 July 2021
  • {{Proth prime |PMultiRes=9
    124 bytes (13 words) - 11:12, 12 July 2021
  • {{Proth prime |PMultiRes=9
    124 bytes (13 words) - 11:12, 12 July 2021
  • {{Proth prime |PMultiRes=9
    124 bytes (13 words) - 11:08, 12 July 2021
  • {{Proth prime |PMultiRes=9
    124 bytes (13 words) - 11:06, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 11:05, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 11:04, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 11:04, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 11:03, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 11:01, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:57, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:56, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:56, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:55, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:54, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:54, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:46, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:44, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:42, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:41, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:40, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:39, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:38, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:36, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:36, 12 July 2021
  • {{Proth prime |PMultiRes=9
    123 bytes (13 words) - 10:35, 12 July 2021
  • {{Proth prime 9;T:T
    278 bytes (33 words) - 15:49, 11 July 2021
  • * 5 ≤ {{Vk}} ≤ 49 for {{Vn}} ≤ 9,000,000, with two exceptions: **{{Vk}} = 9 and 27 did not search even {{Vn}}-values, because they cannot produce Ferma
    4 KB (448 words) - 09:13, 7 September 2021
  • {{Proth prime 4;C:{{NCu|9|2}}
    2 KB (204 words) - 11:06, 18 April 2023
  • {{Proth prime 9
    339 bytes (28 words) - 09:31, 12 July 2021
  • {{Proth prime 9;T:G
    2 KB (236 words) - 02:10, 15 May 2024
  • {{Proth prime 9
    1 KB (116 words) - 03:47, 16 May 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
  • {{Proth prime 9;T:G
    2 KB (275 words) - 04:14, 15 May 2024
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 300 < {{Vk}} < 2000}} Automatically generated table from available [[:Category:Proth 2 300-2000|Proth primes 300 < {{Vk}} < 2000]].
    873 bytes (117 words) - 08:15, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 2000 < {{Vk}} < 4000}} Automatically generated table from available [[:Category:Proth 2 2000-4000|Proth primes 2000 < {{Vk}} < 4000]].
    878 bytes (117 words) - 08:17, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 4000 < {{Vk}} < 6000}} Automatically generated table from available [[:Category:Proth 2 4000-6000|Proth primes 4000 < {{Vk}} < 6000]].
    887 bytes (118 words) - 08:18, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 6000 < {{Vk}} < 8000}} Automatically generated table from available [[:Category:Proth 2 6000-8000|Proth primes 6000 < {{Vk}} < 8000]].
    887 bytes (118 words) - 08:20, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 8000 < {{Vk}} < 10000}} Automatically generated table from available [[:Category:Proth 2 8000-10000|Proth primes 8000 < {{Vk}} < 10000]].
    883 bytes (117 words) - 08:21, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Num|10000}} &le; {{Vk}} &le; {{Num|1000 Automatically 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
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>5</sup> < {{Vk}} < 10<sup>6</sup>} Automatically generated 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
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>6</sup> < {{Vk}} < 10<sup>7</sup>} Automatically generated table from available [[:Category:Proth 2 10e6-10e7|Proth primes 10<sup>6</sup> < {{Vk}} < 10<sup>7</sup>]].
    1 KB (153 words) - 08:33, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>7</sup> < {{Vk}} < 10<sup>8</sup>} Automatically generated table from available [[:Category:Proth 2 10e7-10e8|Proth primes 10<sup>7</sup> < {{Vk}} < 10<sup>8</sup>]].
    1 KB (153 words) - 08:34, 26 July 2021
  • ...TLE:Proth primes of the form {{Kbn|k|n}}, 10<sup>8</sup> < {{Vk}} < 10<sup>9</sup>}} ...[:Category:Proth 2 10e8-10e9|Proth primes 10<sup>8</sup> < {{Vk}} < 10<sup>9</sup>]].
    1 KB (153 words) - 08:35, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>9</sup> < {{Vk}} < 10<sup>10</sup>}} ...ed table from available [[:Category:Proth 2 10e9-10e10|Proth primes 10<sup>9</sup> < {{Vk}} < 10<sup>10</sup>]].
    1 KB (153 words) - 08:36, 26 July 2021
  • {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Vk}} > 10<sup>10</sup>}} ...atically generated table from available [[:Category:Proth 2 10e10-infinity|Proth primes {{Vk}} > 10<sup>10</sup>]].
    1 KB (146 words) - 08:38, 26 July 2021
  • {{Proth prime 9;T:G
    940 bytes (120 words) - 04:12, 15 May 2024
  • |category=Proth 3 |titlematch=Proth prime%
    405 bytes (56 words) - 22:02, 1 August 2021
  • {{Proth prime 9
    754 bytes (79 words) - 09:40, 14 May 2024
  • {{Proth prime 9;T:T
    4 KB (437 words) - 09:15, 14 May 2024
  • {{Proth prime 9;T:T
    584 bytes (57 words) - 16:02, 15 May 2024
  • {{Proth prime 9;T:T
    3 KB (321 words) - 10:00, 14 May 2024
  • {{Proth prime 9
    4 KB (381 words) - 09:07, 14 May 2024
  • {{Proth prime 9;T:G
    1,006 bytes (96 words) - 09:30, 14 May 2024
  • {{Proth prime 9
    1 KB (113 words) - 09:04, 14 May 2024
  • {{Proth prime 9
    2 KB (162 words) - 09:27, 14 May 2024
  • {{Proth prime 2;T:T;C:Is {{DGF|1|10|9}}
    3 KB (389 words) - 01:56, 15 May 2024
  • {{Proth prime 9
    701 bytes (80 words) - 19:38, 5 April 2023
  • {{Proth prime 9
    831 bytes (93 words) - 13:46, 7 April 2023
  • {{Proth prime |PRemarks= 314159265 are first 9 digits of pi
    515 bytes (26 words) - 19:18, 14 March 2024
  • {{Proth prime 9
    4 KB (446 words) - 00:50, 15 May 2024