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  • ...}. On the other hand, 15 = 16 − 1 = {{Kbn|4}}, for example, is not a prime, because 15 is divisible by 3 and 5. ...ion; in the 4th century BC [[Euclid]] demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. Two millennia later, in the 18th century
    5 KB (857 words) - 14:53, 19 September 2021
  • {{Riesel prime {{HistF|2004-11-13|227144|Maksym Voznyy}}
    403 bytes (26 words) - 18:40, 2 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> '''LLR (Lucas Lehmer Riesel)''' is probably the fastest [[Primality testing program|program]] available
    2 KB (300 words) - 22:00, 16 December 2023
  • ...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
  • ..., 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime. | 4 || 11 || {{NRi|3|2}}
    1 KB (171 words) - 04:26, 3 November 2020
  • 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
  • {{DISPLAYTITLE:Riesel problem, {{Kbn|-|k|2|n}}, {{Vk}} < {{Num|509203}}}} The '''Riesel problem''' involves determining the smallest [[Riesel number]].
    6 KB (689 words) - 18:14, 4 April 2024
  • {{Riesel prime 11
    5 KB (523 words) - 09:47, 5 October 2023
  • {{Riesel prime 12;C:{{NWo|-|11}}
    2 KB (196 words) - 18:36, 9 October 2021
  • {{Riesel prime {{HistC|2010-04-11|2510000|Predrag Minovic|211346}}
    3 KB (264 words) - 22:08, 5 July 2023
  • {{Riesel prime |RDate=2021-11-22
    2 KB (252 words) - 13:29, 5 May 2024
  • {{Riesel prime {{HistF|2011-11-21|861356|Michael Curtis|279428}}
    3 KB (329 words) - 07:59, 17 August 2021
  • {{Riesel prime {{HistF|2011-11-19|699676|Peter Benson|279184}}
    2 KB (185 words) - 04:16, 5 May 2024
  • {{Riesel prime {{HistC|2018-11-30|1880000|Borys Jaworski|501366}}
    3 KB (327 words) - 05:57, 19 April 2024
  • {{Riesel prime 11
    2 KB (228 words) - 19:30, 19 July 2023
  • {{Riesel prime {{HistC|2013-06-11|2370000|Michael Curtis|343033}}
    2 KB (184 words) - 22:47, 18 April 2024
  • {{Riesel prime 11
    2 KB (224 words) - 06:12, 9 May 2024
  • {{Riesel prime {{HistC|2020-03-11|6000000|Dmitry Domanov|539375}}
    4 KB (357 words) - 23:04, 19 April 2024
  • {{Riesel prime {{HistF|2003-11-24|429318|Peter Grobstich}}
    2 KB (174 words) - 18:41, 5 May 2024
  • {{Riesel prime {{HistC|2020-03-11|6000000|Dmitry Domanov|539375}}
    3 KB (295 words) - 22:47, 5 July 2023
  • {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|b|n}}, least {{Vn}}-values}} Here are shown the least {{Vn}} &ge; 1 generating a [[Riesel prime]] of the form {{Kbn|k|b|n}} for 2 &le; {{Vb}} &le; 1030 and 2 &le; {{Vk}} &
    6 KB (684 words) - 09:40, 17 March 2024
  • {{Riesel prime {{HistF|2020-11-12|3080952|Thomas Ritschel, RPS Megabit Drive 1|563003}}
    2 KB (222 words) - 06:13, 9 May 2024
  • {{Riesel prime {{HistR|2006-11-12|RPS Drive 5|91301}}, for {{Vn}} > 398000
    2 KB (202 words) - 08:31, 16 May 2024
  • {{Riesel prime {{HistF|1998-12-11|47974|Carlos B. Rivera F.}}
    1 KB (126 words) - 03:35, 6 May 2024
  • {{Riesel prime {{HistC|2010-11-11|1000000|NPLB Drive 5|236723}}
    2 KB (157 words) - 10:53, 5 April 2023
  • {{Riesel prime {{HistC|2011-09-11|1100000|Peter Benson|271488}}
    3 KB (249 words) - 13:48, 21 March 2023
  • {{Riesel prime {{HistC|2013-11-19|225000|Alexander Jones}}
    805 bytes (66 words) - 20:38, 16 July 2021
  • {{Riesel prime {{HistF|2010-11-07|790695|Steven Harvey}}
    713 bytes (46 words) - 08:03, 25 January 2024
  • {{Riesel prime {{HistC|2011-11-23|20000|Thomas Ritschel}}
    443 bytes (35 words) - 23:25, 24 July 2021
  • {{Riesel prime {{HistC|2019-11-08|350000|Alexander Jones}}
    621 bytes (42 words) - 16:58, 14 March 2023
  • {{Riesel prime {{HistC|2019-11-08|150000|Alexander Jones}}
    692 bytes (60 words) - 08:15, 25 January 2024
  • {{Riesel prime 11
    823 bytes (62 words) - 08:12, 25 January 2024
  • {{Riesel prime {{HistF|2005-07-11|1195203|Mark Rodenkirch}}
    635 bytes (48 words) - 08:11, 25 January 2024
  • {{Riesel prime {{HistC|2008-11-28|300000|Gary Barnes|151087}},double-check
    241 bytes (24 words) - 00:15, 17 July 2021
  • {{Riesel prime {{HistC|2013-11-11|500000|Alexander Jones}}
    370 bytes (39 words) - 00:06, 17 July 2021
  • {{Riesel prime {{HistC|2013-11-11|500000|Alexander Jones}}
    359 bytes (39 words) - 00:06, 17 July 2021
  • {{Riesel prime {{HistC|2011-11-23|20000|Thomas Ritschel}}
    775 bytes (85 words) - 00:10, 17 July 2021
  • {{Riesel prime {{HistC|2011-11-23|20000|Thomas Ritschel}}
    487 bytes (36 words) - 23:41, 24 July 2021
  • {{Riesel prime |RDate=2018-11-26
    354 bytes (29 words) - 00:23, 17 July 2021
  • {{Riesel prime {{HistF|2001-12-11|146803|Dale Andrews}}
    375 bytes (24 words) - 11:45, 21 July 2021
  • {{Riesel prime 11
    413 bytes (32 words) - 20:34, 31 July 2021
  • {{Riesel prime {{HistC|2011-11-23|1007|Gary Barnes}}
    417 bytes (37 words) - 14:28, 21 July 2021
  • {{Riesel prime {{HistC|2011-11-23|1007|Gary Barnes}}
    409 bytes (32 words) - 10:50, 21 July 2021
  • {{Riesel prime {{HistC|2018-08-11|500000|Alexander Jones}}
    401 bytes (35 words) - 08:06, 25 January 2024
  • {{Riesel prime {{HistF|2012-11-14|1165668|Steven Harvey}}
    480 bytes (40 words) - 08:07, 25 January 2024
  • | 1 || 1 || 1 || {{Kbn|2|1}} || [[Riesel prime 2 1|{{Kbn|2}}]] || n.n. || n.n. | 2 || 2 || 2 || {{Kbn|3|2}} || [[Riesel prime 2 3|{{Kbn|3|2}}]] || n.n. || n.n.
    4 KB (327 words) - 16:31, 31 August 2021
  • {{Riesel prime |RDate=2011-11-23
    405 bytes (32 words) - 14:20, 21 July 2021
  • {{Riesel prime |RCount=11
    679 bytes (81 words) - 21:10, 17 December 2023
  • {{Riesel prime {{HistC|2013-11-19|225000|Alexander Jones}}
    906 bytes (79 words) - 10:12, 15 March 2024
  • | 1 || 2 || 1 || {{Kbn|1|2}} || [[Riesel prime 2 1|{{Kbn|2}}]]<ref>Mersenne prime [[M1]]</ref> || n.n. || n.n. | 2 || 4 || 2 || {{Kbn|3|4}} || [[Riesel prime 2 3|{{Kbn|3|4}}]] || n.n. || n.n.
    3 KB (313 words) - 16:51, 31 August 2021
  • {{Riesel prime |Rk=11
    3 KB (280 words) - 00:00, 24 April 2024
  • {{Riesel prime {{HistC|2013-06-11|2980000|Michael Curtis|343033}}
    2 KB (242 words) - 19:29, 19 July 2023
  • {{Riesel prime {{HistF|2012-11-06|2160479|Predrag Minovic|317295}}
    3 KB (285 words) - 08:15, 7 May 2024
  • {{Riesel prime 11
    6 KB (613 words) - 05:54, 19 April 2024
  • {{Riesel prime {{HistC|2022-03-21|10000000|PrimeGrid 27121 Prime Search|P#9850#154888}}, released
    3 KB (341 words) - 08:00, 12 April 2023
  • {{Riesel prime |RDate=2021-11-10
    1 KB (105 words) - 23:07, 22 November 2021
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    2 KB (238 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistC|2011-11-23|20000|Thomas Ritschel}}
    439 bytes (29 words) - 03:41, 26 July 2021
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    2 KB (188 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistF|2015-11-11|2251104|Michael Kwok|415858}}
    2 KB (202 words) - 11:02, 19 March 2024
  • {{Riesel prime {{HistC|2016-11-30|5030000|Borys Jaworski|448104}}
    5 KB (539 words) - 14:34, 19 April 2024
  • {{Riesel prime {{HistF|2014-11-30|1957377|Michael Curtis|388766}}
    3 KB (310 words) - 19:32, 19 July 2023
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    1 KB (118 words) - 02:40, 12 May 2024
  • {{Riesel prime {{HistC|2017-11-02|4610000|David Metcalfe|470845}}
    3 KB (317 words) - 10:28, 15 July 2021
  • {{Riesel prime {{HistC|2014-08-11|5100000|Peter Riesen|380194}}, released
    2 KB (219 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    1 KB (133 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistC|2010-11-30|1320000|Borys Jaworski|239400}}
    2 KB (226 words) - 08:15, 7 May 2024
  • {{Riesel prime {{HistF|2020-11-12|3093440|Thomas Ritschel, RPS Megabit Drive 1|563003}}
    2 KB (224 words) - 02:42, 12 May 2024
  • {{Riesel prime {{HistC|2010-04-11|3410000|Borys Jaworski|211365}}, released
    2 KB (157 words) - 08:17, 7 May 2024
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    2 KB (208 words) - 02:44, 12 May 2024
  • {{Riesel prime {{HistC|2013-11-01|2960000|David Metcalfe|360804}}
    2 KB (171 words) - 10:45, 15 July 2021
  • {{Riesel prime 11
    4 KB (392 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistC|2020-03-11|6000000|Dmitry Domanov|539375}}
    930 bytes (97 words) - 12:03, 15 July 2021
  • {{Riesel prime 11
    1 KB (153 words) - 10:22, 8 October 2022
  • {{Riesel prime {{HistC|2011-07-11|2000000|Larry Soule|266114}}
    2 KB (246 words) - 08:18, 7 May 2024
  • {{Riesel prime {{HistC|2004-11-04|480000|Predrag Minovic|44306}}
    2 KB (179 words) - 10:44, 26 April 2024
  • {{Riesel prime {{HistC|2016-11-30|3580000|Borys Jaworski|448104}}
    4 KB (406 words) - 12:09, 15 July 2021
  • {{Riesel prime 11
    2 KB (226 words) - 08:39, 7 May 2024
  • {{Riesel prime {{HistC|2021-11-14|3700000|Erling Bergþórsson|593096}}
    3 KB (272 words) - 20:45, 26 February 2024
  • {{Riesel prime 11
    1 KB (152 words) - 10:44, 26 April 2024
  • {{Riesel prime {{HistC|2018-04-11|3000000|RPS Megabit Drive 1|485017}}
    3 KB (279 words) - 13:33, 5 May 2024
  • {{Riesel prime {{HistR|2020-11-21|Vincent Diepeveen|563943}}
    2 KB (187 words) - 12:37, 15 July 2021
  • {{Riesel prime {{HistC|2010-02-11|1120000|Predrag Minovic|205283}}, released
    2 KB (208 words) - 06:58, 24 April 2024
  • {{Riesel prime {{HistF|2016-11-04|2708718|Michael Curtis|446423}}
    3 KB (249 words) - 23:57, 23 April 2024
  • {{Riesel prime {{HistC|2010-04-11|1100000|Predrag Minovic|211346}}
    1 KB (147 words) - 07:28, 24 April 2024
  • {{Riesel prime {{HistC|2010-04-11|1150000|Predrag Minovic|211346}}
    1 KB (128 words) - 00:04, 24 April 2024
  • {{Riesel prime 11;T:T
    3 KB (266 words) - 19:34, 19 July 2023
  • {{Riesel prime {{HistC|2018-11-30|6280000|Borys Jaworski|501365}}
    5 KB (535 words) - 07:13, 19 July 2021
  • {{Riesel prime 11
    2 KB (222 words) - 13:33, 5 May 2024
  • {{Riesel prime |RDate=2018-12-11
    2 KB (207 words) - 08:48, 19 July 2021
  • {{Riesel prime {{HistC|2012-11-06|1100000|Adam Sutton|317245}}, released
    1 KB (104 words) - 08:48, 19 July 2021
  • {{Riesel prime {{HistC|2013-06-11|1620000|Michael Curtis|343033}}
    1 KB (146 words) - 19:35, 19 July 2023
  • {{Riesel prime {{HistF|2020-11-12|3060238|Thomas Ritschel, RPS Megabit Drive 1|563003}}
    4 KB (361 words) - 04:54, 9 May 2024
  • {{Riesel prime {{HistC|2018-04-11|6000000|Thomas Ritschel|485018}}
    2 KB (221 words) - 00:05, 24 April 2024
  • {{Riesel prime 11
    2 KB (153 words) - 08:28, 16 May 2024
  • {{Riesel prime {{HistF|2013-11-15|1554601|Predrag Kurtovic, RPS Megabit Drive 2|359412}}
    2 KB (242 words) - 08:29, 16 May 2024
  • {{Riesel prime {{HistF|2018-11-29|3571416|Thomas Ritschel|501238}}
    2 KB (180 words) - 00:01, 24 April 2024
  • {{Riesel prime {{HistC|2021-04-08|10000000|PrimeGrid 27121 Prime Search|P#9612#149921}}
    1 KB (121 words) - 09:13, 29 September 2021
  • {{Riesel prime 11
    2 KB (230 words) - 08:30, 16 May 2024

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