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  • GMP-ECM
    ....tar.bz2 MPIR] and [https://gforge.inria.fr/frs/download.php/30965/ecm-6.4.3.tar.gz GMP-ECM] (don't unpack them, just place them on your desktop). 3. Now move the MPIR and GMP-ECM to C:\YourMsysDirectory\1.0\home\YourUser\.
    4 KB (567 words) - 10:54, 6 December 2019
  • Gerbicz error checking
    # <math>d(j)</math> (for identity (3)) ...<math>n/L</math> [[Modular arithmetic#Modular multiplication|mulmods]] in (3) and <math>n / L^2 * L = n/L</math> [[Modular arithmetic#Modular exponentia
    3 KB (528 words) - 14:59, 3 October 2023
  • System requirements and compatible hardware
    :Windows NT (3 / 4 / 4 SP 1 / 4 SP 2 / 4 SP 3 / 4 SP 4 / 4 SP 5 / 4 SP 6) :Windows 2000 (SP 1 / SP 2 / SP 3 / SP 4)
    766 bytes (95 words) - 12:25, 19 February 2019
  • PrimeNet summary report
    ...st vertical divider is the '''Exponent Range''' section and is broken into 3 columns.
    7 KB (1,073 words) - 08:46, 15 May 2024
  • Square number
    ...two square integers is also a square number (e.g. 2/3&nbsp;&times;&nbsp;2/3 = 4/9). :3<sup>2</sup> = 9
    3 KB (408 words) - 13:56, 19 February 2019
  • Sierpiński number base 5
    ...i problem]] article, it was found that {{Kbn|+|159986|5|n}} is multiple of 3, 7, 13, 31 or 601 (the [[covering set]]) depending on the value of {{Vn}},
    556 bytes (83 words) - 10:57, 14 October 2020
  • Riesel number base 5
    ...l problem]] article, it was found that {{Kbn|-|346802|5|n}} is multiple of 3, 7, 13, 31 or 601 (the [[covering set]]) depending on the value of n, so it
    589 bytes (90 words) - 10:30, 26 March 2024
  • Riesel problem 1
    | 2 || 3 || {{Num|214734}} || {{Num|{{PAGESINCATEGORY:Riesel 2 1Intervals1|pages|R}} ! scope="row" | [[:Category:Riesel 2 1Intervals3|3]]
    6 KB (689 words) - 18:14, 4 April 2024
  • Peano postulates
    ...; it characterises the set (class, condition) of [[natural number]]s 1, 2, 3, etc., and consists of the following '''Peano postulates''' (also called ''
    2 KB (269 words) - 17:04, 24 October 2020
  • Mersenne.ca
    ...g of the 1000M to 4294M range in September 2012 eliminated approximately 1/3 of the candidates (roughly 50 million factors from approximately 150 millio
    9 KB (1,396 words) - 15:42, 25 February 2019
  • Aurifeuillian factor
    **<math>t\equiv 2, 3 \pmod 4</math> and <math>n\equiv 2t \pmod{4t}</math> ....edu/~ssw/cun/pmain1215 Main Cunningham Tables]. At the end of tables 2LM, 3+, 5-, 6+, 7+, 10+, 11+ and 12+ are formulae detailing the Aurifeuillian fac
    10 KB (1,257 words) - 08:04, 24 June 2019
  • Cullen number
    ...me/guenter/gc/status.html Generalized Cullen Search, G&uuml;nter L&ouml;h (3 &le; base &le; 100), dated Sept. 2017]
    2 KB (252 words) - 17:39, 31 August 2021
  • Carol-Kynea prime 8
    |CKMaxn={{#expr:floor({{GP|Carol-Kynea prime 2|CKMaxn}}/3)}} |CKClist={{Reuse Primelist|Carol-Kynea prime 2|CKClist|3}}
    389 bytes (47 words) - 10:33, 10 June 2019
  • Carol-Kynea prime 290
    3
    1 KB (119 words) - 19:02, 21 June 2021
  • Multifactorial number
    :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> :<math>n!!! = (n) \cdot (n-3) \cdot (n-6) \cdots</math>
    560 bytes (81 words) - 14:36, 20 July 2021
  • Riesel prime 2 1
    3;T:W;C:'''[[M2]]''', {{NWo|2}}, {{NWo|8|1}} 5;C:'''[[M3]]''', {{NWo|+|3}}, {{NWo|4|2}}, {{NWo|32|1}}
    2 KB (288 words) - 11:41, 3 April 2023
  • Riesel prime 2 3
    |Rk=3 3;T:SW;C:{{NWo|3}}
    5 KB (523 words) - 09:47, 5 October 2023
  • Riesel prime 2 2145
    3;T:S
    4 KB (329 words) - 10:10, 31 May 2024
  • Carol-Kynea prime 50
    3
    490 bytes (45 words) - 12:30, 3 July 2019
  • Williams prime MM 10
    3
    1 KB (143 words) - 02:41, 5 November 2020
  • Williams prime PM 2
    |WiMaxn={{GP|Riesel prime 2 3|RMaxn}} |WiDate={{GP|Riesel prime 2 3|RDate}}
    246 bytes (35 words) - 14:04, 1 August 2021
  • Williams prime PP 2
    |WiMaxn={{GP|Proth prime 2 3|PMaxn}} |WiDate={{GP|Proth prime 2 3|PDate}}
    259 bytes (36 words) - 10:52, 13 July 2021
  • Williams prime MM 4
    |WiMaxn={{#expr:floor({{GP|Riesel prime 2 3|RMaxn}}/2)}} |WiDate={{GP|Riesel prime 2 3|RDate}}
    265 bytes (37 words) - 20:50, 31 July 2021
  • Williams prime MM 3
    |WiBase=3 |WiMaxn={{GP|Riesel prime 3 2|RMaxn}}
    248 bytes (35 words) - 09:56, 16 March 2023
  • Williams prime PM 3
    |WiBase=3 |WiMaxn={{GP|Riesel prime 3 4|RMaxn}}
    248 bytes (35 words) - 13:40, 16 March 2023
  • Williams prime MM 8
    |WiMaxn={{#expr:floor({{GP|Riesel prime 2 7|RMaxn}}/3)}} |WiNlist={{Reuse Primelist|Riesel prime 2 7|RNlist|3}}
    291 bytes (42 words) - 20:52, 31 July 2021
  • Williams prime MM 9
    |WiRemarks=Should be (re)used from {{NRi|8|3|n}}.<br>The {{OEIS|l|A268356}} and halved even values of {{OEIS|l|A005541}}
    412 bytes (45 words) - 20:59, 31 July 2021
  • Williams prime MM 11
    3
    366 bytes (36 words) - 20:54, 31 July 2021
  • Williams prime MM 14
    3
    402 bytes (44 words) - 11:53, 21 May 2019
  • Williams prime MM 17
    3
    214 bytes (19 words) - 12:20, 21 May 2019
  • Williams prime MM 27
    3 |WiRemarks=Should be (re)used from {{NRi|26|3|n}}.
    282 bytes (26 words) - 20:58, 31 July 2021
  • Proth prime 2 3
    |Pk=3
    3 KB (336 words) - 16:58, 15 April 2024
  • Generalized Fermat number 12 5 1
    |GFNDigits=3 3,2
    128 bytes (12 words) - 09:57, 30 July 2021
  • Generalized Fermat number 12 7 1
    |GFNDigits=3
    125 bytes (12 words) - 15:10, 17 August 2021
  • GF Divisor 3 20909
    |GFk=3 3,2,20905#1996#Anders Björn,Hans Riesel
    656 bytes (73 words) - 21:56, 16 August 2021
  • GF Divisor 46409657301841 16
    3,1,15#2008#Geoffrey Reynolds
    153 bytes (10 words) - 08:55, 23 September 2021
  • Proth prime 2 5
    3;T:G
    1 KB (148 words) - 13:21, 26 May 2024
  • Proth prime 2 9
    3;T:GT
    3 KB (456 words) - 04:11, 15 May 2024
  • GF Divisor 9 6
    9,8,3#1996#Anders Björn,Hans Riesel
    264 bytes (33 words) - 17:56, 23 August 2021
  • GF Divisor 9 7
    3,2,5#1996#Anders Björn,Hans Riesel
    305 bytes (38 words) - 18:11, 23 August 2021
  • Proth prime 2 11
    3;T:G
    2 KB (252 words) - 13:26, 26 May 2024
  • Proth prime 2 17
    3;T:G
    1 KB (153 words) - 13:30, 26 May 2024
  • Proth prime 2 1527888802614951
    3
    375 bytes (33 words) - 09:10, 17 May 2024
  • Sieving a range of sequences
    Sieving a range {{Kbn|3|2|n}} to {{Kbn|20|19|n}} (in general {{Kbn|(b+1)|b|n}}) create a batch file
    775 bytes (124 words) - 08:39, 22 April 2019
  • LLR testing a range of sequences
    Testing a range {{Kbn|3|2|n}} to {{Kbn|20|19|n}} (in general {{Kbn|(b+1)|b|n}}) create a batch file
    871 bytes (147 words) - 12:29, 23 April 2019
  • Carol-Kynea prime 12
    3
    713 bytes (72 words) - 16:32, 12 February 2020
  • Carol-Kynea prime 22
    3
    362 bytes (28 words) - 15:25, 15 July 2019
  • Carol-Kynea prime 30
    3
    450 bytes (38 words) - 01:20, 8 July 2019
  • Woodall prime 6
    3
    593 bytes (52 words) - 10:32, 17 August 2023
  • Woodall prime 4
    2;C:{{NRi|5}}, {{NWo|+|3}} 3;T:T;C:{{NRi|3|6}}, {{NWo|+|5}}
    1 KB (122 words) - 17:00, 31 August 2021
  • Woodall prime 3
    |WoBase=3 2;T:T;C:{{NRi|2|3|2}}
    1 KB (115 words) - 07:13, 17 August 2023
  • Woodall prime 2
    2;C:{{NRi|3}} 3;C:{{NRi|3|3}}
    2 KB (230 words) - 10:36, 27 March 2023
  • Woodall prime 8
    1;C:{{NRi|3}} 12;C:{{NRi|3|38}}
    702 bytes (72 words) - 10:58, 17 August 2023
  • Woodall prime 9
    10;C:{{NRi|10|3|20}} 58;C:{{NRi|58|3|116}}
    469 bytes (46 words) - 21:51, 28 February 2024
  • Woodall prime 10
    3
    684 bytes (71 words) - 08:21, 30 April 2023
  • Cullen prime 3
    |CuBase=3 54;C:{{NPr|2|3|57}}
    697 bytes (65 words) - 18:55, 19 July 2023
  • Cullen prime 4
    3;C:{{NPr|3|6}}
    849 bytes (85 words) - 19:15, 14 July 2023
  • Carol-Kynea prime 42
    3 3
    882 bytes (79 words) - 08:41, 15 October 2021
  • Carol-Kynea prime 44
    3
    423 bytes (36 words) - 12:34, 1 July 2019
  • Carol-Kynea prime 1968
    3
    352 bytes (31 words) - 11:43, 4 July 2019
  • Williams prime PP least
    Values of bases {{Vb}} ≡ 1 mod 3 are always divisible by 3, so not listed here.
    2 KB (306 words) - 03:50, 28 May 2024
  • Williams prime MP 3
    |WiBase=3 4217;35890;C:Divides Phi(3^4217,2)
    2 KB (151 words) - 00:47, 25 May 2020
  • Williams prime MM 33
    3
    210 bytes (19 words) - 21:30, 16 May 2019
  • Williams prime MM 35
    3
    209 bytes (19 words) - 21:40, 16 May 2019
  • Williams prime MM 39
    3
    215 bytes (19 words) - 08:44, 17 May 2019
  • Williams prime MM 42
    3
    196 bytes (17 words) - 09:38, 17 May 2019
  • Williams prime MM 46
    3
    195 bytes (17 words) - 09:49, 17 May 2019
  • Williams prime MM 48
    3
    184 bytes (17 words) - 09:53, 17 May 2019
  • Williams prime MM 53
    3
    168 bytes (17 words) - 10:51, 17 May 2019
  • Williams prime MM 57
    3
    170 bytes (17 words) - 10:58, 17 May 2019
  • Williams prime MM 59
    3
    171 bytes (17 words) - 11:00, 17 May 2019
  • Williams prime MM 63
    3
    212 bytes (19 words) - 11:33, 17 May 2019
  • Riesel prime 2 63
    3
    2 KB (224 words) - 06:12, 9 May 2024
  • Williams prime MP 4
    |WiMaxn={{Reuse Primelist|Proth prime 2 3|PMaxn|2}} |WiDate={{GP|Proth prime 2 3|PDate}}
    258 bytes (36 words) - 08:07, 1 August 2021
  • Williams prime MP 8
    |WiMaxn={{Reuse Primelist|Proth prime 2 7|PMaxn|3}} |WiNlist={{Reuse Primelist|Proth prime 2 7|PNlist|3}}
    284 bytes (41 words) - 08:16, 1 August 2021
  • Williams prime MP 9
    |WiMaxn={{#expr:floor({{GP|Proth prime 3 8|PMaxn}}/2)}} |WiDate={{GP|Proth prime 3 8|PDate}}
    387 bytes (53 words) - 08:30, 12 July 2021
  • Williams prime MP 10
    3
    1 KB (136 words) - 07:35, 16 May 2024
  • Williams prime MP 12
    3
    210 bytes (20 words) - 09:46, 20 May 2019
  • Williams prime PM 6
    3
    499 bytes (40 words) - 20:46, 21 May 2024
  • Riesel prime 2 9
    3;T:T
    4 KB (357 words) - 23:04, 19 April 2024
  • Williams prime PM 8
    |WiMaxn={{#expr:floor({{GP|Riesel prime 2 9|RMaxn}}/3)}} |WiNlist={{Reuse Primelist|Riesel prime 2 9|RNlist|3}}
    265 bytes (37 words) - 14:09, 1 August 2021
  • Williams prime PM 9
    |WiRemarks=This list should be a (re)use of {{Kbn|10|3|n}}!<br>Halved even values of the {{OEIS|l|A005542}}
    428 bytes (42 words) - 22:03, 20 April 2024
  • Williams prime PM 11
    3
    250 bytes (17 words) - 11:02, 23 May 2019
  • Williams prime MM 88
    3
    173 bytes (16 words) - 13:38, 21 May 2019
  • Williams prime MP 15
    3
    290 bytes (23 words) - 19:22, 30 September 2020
  • Williams prime MP 21
    3
    313 bytes (23 words) - 18:30, 19 November 2020
  • Williams prime MP 27
    |WiMaxn={{#expr:floor({{GP|Proth prime 3 26|PMaxn}}/3)}} |WiDate={{GP|Proth prime 3 26|PDate}}
    443 bytes (56 words) - 08:44, 12 July 2021
  • Williams prime PM 13
    3
    221 bytes (17 words) - 11:11, 23 May 2019
  • Williams prime PM 18
    3
    218 bytes (18 words) - 12:46, 23 May 2019
  • Williams prime PM 24
    3
    230 bytes (18 words) - 13:16, 23 May 2019
  • Williams prime PM 27
    |WiRemarks=Should be (re)used from {{Kbn|28|3|n}}.
    277 bytes (26 words) - 13:23, 23 May 2019
  • Riesel prime 2 33
    3
    3 KB (295 words) - 22:47, 5 July 2023
  • Williams prime PM 38
    3
    232 bytes (18 words) - 14:14, 23 May 2019
  • Williams prime PM 107
    3
    197 bytes (18 words) - 14:22, 23 May 2019
  • Williams prime PM 113
    3
    221 bytes (18 words) - 14:23, 23 May 2019
  • Williams prime PP 3
    |WiBase=3 |WiMaxn={{GP|Proth prime 3 4|PMaxn}}
    293 bytes (41 words) - 11:57, 13 July 2021
  • Williams prime PP 5
    3
    567 bytes (52 words) - 06:08, 18 June 2020
  • Williams prime PP 8
    |WiMaxn={{#expr:floor({{GP|Proth prime 2 9|PMaxn}}/3)}} |WiNlist={{Reuse Primelist|Proth prime 2 9|PNlist|3}}
    278 bytes (38 words) - 11:59, 13 July 2021
  • Williams prime PP 9
    |WiMaxn={{#expr:floor({{GP|Proth prime 3 10|PMaxn}}/2)}} |WiDate={{GP|Proth prime 3 10|PDate}}
    268 bytes (37 words) - 08:34, 12 July 2021
  • Williams prime PP 11
    3
    234 bytes (19 words) - 16:38, 26 May 2019

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