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  • ...de=true|title=Example of prime sequence and reservation|content=[[Williams prime MM 5]]}} *[https://www.rieselprime.de/default.htm Riesel and Proth Prime Databse RPPDb]
    11 KB (1,236 words) - 14:41, 3 September 2020
  • *{{Kbn|+|78557|12n+11}} is multiple of 13. (those values form a [[covering set]] of {3, 5, 7, 13, 19, 37, 73}) we can prepare the following table for the exponents modulo 3
    5 KB (650 words) - 10:25, 26 March 2024
  • ...: "The test that we today call Pépin's test is actually [[Proth's theorem|Proth's test]] with a proof provided by Lucas". Pépin's test says: If <math>n>0</math>, <math>F_n = 2^{2^n}+1</math> is a prime if and only if <math>\ 3^{(F_n-1)/2} \ \equiv -1 \ \pmod{F_n}</math>.
    2 KB (401 words) - 14:40, 6 March 2019
  • {{Proth prime 13;T:G
    1 KB (144 words) - 11:12, 24 August 2021
  • {{Proth prime {{HistF|2020-03-13|11500843|Ryan Propper}}
    3 KB (432 words) - 18:48, 9 April 2023
  • {{Proth prime |Pk=13
    1 KB (175 words) - 07:07, 25 August 2021
  • {{Proth prime 13;T:G
    2 KB (202 words) - 11:31, 31 August 2021
  • {{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 13
    3 KB (289 words) - 10:52, 21 September 2021
  • {{Proth prime {{HistF|2020-07-13|1700041|Paul Vanderveen|550507}}
    1 KB (124 words) - 08:43, 12 July 2021
  • {{Proth prime 13
    582 bytes (53 words) - 10:16, 12 July 2021
  • {{Proth prime |PDate=2020-09-13
    657 bytes (66 words) - 08:33, 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 13
    877 bytes (71 words) - 00:12, 30 April 2024
  • {{Proth prime 13;T:T
    278 bytes (33 words) - 15:49, 11 July 2021
  • *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 {{HistF|2010-02-13|1086112|David Broadhurst}}
    2 KB (204 words) - 11:06, 18 April 2023
  • {{Proth prime |PDate=2020-11-13
    288 bytes (26 words) - 10:19, 12 July 2021
  • {{Proth prime 13
    391 bytes (32 words) - 10:04, 12 July 2021
  • {{Proth prime {{HistF|2019-09-13|3124079|Dave Sunderland,PrimeGrid}}
    677 bytes (57 words) - 08:55, 18 September 2021
  • {{Proth prime 13;T:G
    2 KB (228 words) - 10:04, 1 September 2021
  • {{Proth prime 13
    872 bytes (112 words) - 09:54, 1 September 2021
  • {{Proth prime {{HistF|2019-10-13|4532463|Jack Harris,PrimeGrid Fermat Divisor Search}}
    2 KB (269 words) - 15:14, 30 August 2021
  • *[[Riesel prime 2 27]] *[[Proth prime 2 27]]
    949 bytes (108 words) - 13:34, 5 November 2023
  • {{Proth prime |PDate=2021-08-13
    429 bytes (29 words) - 09:47, 13 August 2021
  • {{Proth prime {{HistF|2021-07-22|3069884|Toshiya Satoh,PrimeGrid Proth Prime Search}}
    1 KB (123 words) - 15:54, 15 August 2021
  • {{Proth prime {{HistF|2021-05-12|3033775|Stefan Larsson,PrimeGrid Proth Prime Search}}
    2 KB (152 words) - 10:56, 17 September 2021
  • {{Proth prime 13
    612 bytes (62 words) - 14:00, 3 September 2021
  • {{Proth prime 13
    2 KB (175 words) - 06:23, 14 May 2024
  • {{Proth prime 13
    2 KB (154 words) - 04:54, 21 September 2021
  • {{Proth prime {{HistC|2024-04-30|5000000|PrimeGrid Proth Prime Search}}
    1 KB (101 words) - 01:44, 14 May 2024
  • {{Proth prime {{HistC|2023-04-30|4000000|PrimeGrid Proth Prime Search}}
    2 KB (214 words) - 06:00, 14 May 2024
  • {{Proth prime {{HistF|2021-07-10|3066009|Ryan Propper,PrimeGrid Proth Prime Search}}
    3 KB (304 words) - 19:58, 13 September 2021
  • {{Proth prime {{HistC|2024-02-29|4500000|PrimeGrid Proth Prime Search}}
    3 KB (286 words) - 04:12, 14 May 2024
  • {{Proth prime {{HistC|2024-04-30|5000000|PrimeGrid Proth Prime Search}}
    1 KB (114 words) - 01:48, 14 May 2024
  • {{Proth prime {{HistF|2021-05-18|3037988|Stefan Larsson,PrimeGrid Proth Prime Search}}
    1 KB (102 words) - 06:42, 20 September 2021
  • {{Proth prime 13;T:T
    2 KB (233 words) - 06:16, 14 May 2024
  • {{Proth prime {{HistC|2024-02-29|4500000|PrimeGrid Proth Prime Search}}
    4 KB (355 words) - 04:18, 14 May 2024
  • {{Proth prime {{HistC|2024-02-29|4500000|PrimeGrid Proth Prime Search}}
    2 KB (186 words) - 04:24, 14 May 2024
  • {{Proth prime {{HistF|2013-04-02|2128328|Ken Micom,PrimeGrid Proth Prime Search}}
    2 KB (251 words) - 22:19, 5 July 2023
  • {{Proth prime 13;T:G
    4 KB (510 words) - 13:09, 27 September 2021
  • {{Proth prime |PCount=13
    684 bytes (69 words) - 06:19, 14 May 2024
  • {{Proth prime {{HistC|2024-02-29|4500000|PrimeGrid Proth Prime Search}}
    3 KB (272 words) - 05:37, 14 May 2024
  • {{Proth prime {{HistC|2024-02-29|4500000|PrimeGrid Proth Prime Search}}
    2 KB (213 words) - 01:55, 14 May 2024
  • {{Proth prime {{HistC|2022-07-31|3322000|PrimeGrid Proth Prime Search}}
    3 KB (254 words) - 06:50, 14 May 2024
  • {{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 {{HistC|2022-07-31|3322000|PrimeGrid Proth Prime Search}}
    986 bytes (93 words) - 06:46, 14 May 2024
  • {{Proth prime {{HistF|2021-09-13|3087514|Andreas H. Mahnken,PrimeGrid Proth Prime Search}}
    1 KB (129 words) - 12:31, 4 October 2021

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