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• Woodall prime M 4
  |WoBase=4
  1 KB (101 words) - 13:56, 15 March 2023
• Proth prime 5 4
  |Pk=4
  718 bytes (75 words) - 07:17, 14 February 2023
• Riesel prime 3 4
  |Rk=4
  4 KB (400 words) - 13:39, 16 March 2023
• Riesel problem 4
  {{DISPLAYTITLE:Riesel problem 4, {{Kbn|-|k|2|n}}, {{Num|777149}} < {{Vk}} < {{Num|790841}}}} | [[:Category:Riesel 2 4Intervals2|2]] || 4 || 7 || {{Num|4416}} || {{Num|{{PAGESINCATEGORY:Riesel 2 4Intervals2|pages|
  4 KB (336 words) - 18:50, 30 April 2024

Page text matches

• M12
  ...} [http://www.garlic.com/~wedgingt/MMPstats.txt], a [[bit level]] over 169.4. The current version of [[Prime95]] cannot handle numbers this large, nor c
  2 KB (354 words) - 14:52, 19 September 2021
• Lucas primality test
  Prove that N = 811 is prime knowing that N-1 = 2 &times; 3⁴ &times; 5
  1 KB (177 words) - 14:31, 17 February 2019
• Square root
  ...= 1 + \frac{1}{2}x - \frac{1}{8}x^2 + \frac{1}{16} x^3 - \frac{5}{128} x^4 + ...</math> <u> 1 2. 3 4 </u>
  13 KB (1,873 words) - 16:52, 24 October 2020
• Pépin's test
  ...of other numbers, like the [[Generalized 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
• Proof by induction
  ...ally taken to be 1, but that is not essential. In some proofs (see example 4 below) we have to show that the statement is true for several values of n. :<math>\sum_{k=1}^{n}k^{3}\,=\,\frac{n^{2}(n+1)^{2}}{4}</math>
  4 KB (679 words) - 13:57, 20 February 2019
• Pseudoprime
  ...of the Miller-Rabin test, for example, has a probability of only <math>{1/4}^{100}</math> of being composite, which is less than <math>10^{-60}</math>.
  1 KB (155 words) - 20:32, 25 July 2020
• Modular square root
  ===Modulus congruent to 3 modulo 4=== :<math>r\equiv \pm a^{(m+1)/4}\ \pmod m</math>
  5 KB (726 words) - 10:38, 6 February 2019
• Legendre symbol
  ...es} 1 & \text{if } p \equiv 1 \pmod{4} \\ -1 & \text{if } p \equiv 3 \pmod{4} \end{cases}</math> ...property is known as the [[law of quadratic reciprocity]]. The properties 4 and 5 are traditionally known as the ''supplements'' to quadratic reciproci
  2 KB (348 words) - 18:57, 28 September 2023
• Law of quadratic reciprocity
  *If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if *If both of <math>p</math> or <math>q</math> are congruent to 3 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if
  1 KB (208 words) - 18:19, 2 October 2022
• Double Mersenne number
  This holds true for the first 4 terms: However this does not hold true for next 4 terms:
  4 KB (655 words) - 14:50, 19 September 2021
• Self-initializing quadratic sieve
  :<math>45^2\,\equiv \,2^4*7^0*13^1</math>
  10 KB (1,763 words) - 02:56, 12 March 2019
• Miller-Rabin pseudoprimality test
  ...strated that a composite <math>N</math> will only pass at most <math>(N-1)/4</math> such tests. ...35. Since the exponent is 4, the sequence will use exponents from zero to 4.
  3 KB (432 words) - 15:33, 28 January 2019
• Generalized Fermat number
  3*2^41+1 is a Factor of xGF(38,4,3)!!!! (0.000000 seconds)
  5 KB (726 words) - 09:57, 12 September 2021
• Patrick Laroche
  ...hunting on his media server to "give back" to the project. After less than 4 months and on just his fourth try, he discovered the new prime number. By w
  987 bytes (147 words) - 01:27, 15 January 2024
• Top GIMPS teams
  | 4 || [[Team Prime Rib|Ars Technica Team Prime Rib]] || 4457877
  2 KB (206 words) - 09:56, 7 March 2019
• Aliquot sequence
  :<math>s_1\ =\ 18\ -\ 10\ =\ 8,\ \sigma(8)\ =\ 1\ +\ 2\ +\ 4\ +\ 8</math> :<math>2^4\ *\ 31</math>
  6 KB (914 words) - 19:49, 21 February 2023
• Abundant number
  The divisors of 12 are <math>(1, 2, 3, 4, 6, 12)</math>, so :<math>\sigma(12)\ =\ 1+2+3+4+6+12\ =\ 28</math>
  671 bytes (92 words) - 00:34, 30 January 2019
• Prime
  ...whole numbers from 2 to P plus the number 1. In other words, Q = (2 x 3 x 4 x 5 ... x P) + 1. From the form of the number Q, it is obvious that no inte :the remainder r can be only 0, 1, 2, 3, 4, or 5
  2 KB (447 words) - 00:22, 10 July 2023
• Twin prime
  | align="right" | 10⁴ || align="right" | 205
  2 KB (255 words) - 06:08, 21 February 2023
• Proth prime 2 28831
  4
  581 bytes (64 words) - 19:18, 5 April 2023
• Why participate in GIMPS?
  ...d 28 who are equal to the sum of their aliquot divisors: 6 = 1+2+3, 28=1+2+4+7+14). He realized that the even perfect numbers (no odd perfect numbers ar
  7 KB (1,252 words) - 09:47, 7 March 2019
• Sophie Germain prime
  | 4 || 11 || {{NRi|3|2}} | 17 || 239 || {{NRi|15|4}}
  1 KB (171 words) - 04:26, 3 November 2020
• Torture test
  ...sing the default "Blend" setting, the first instance each will use about 3/4 of memory the system memory. The second instance will try to do the same. T
  2 KB (323 words) - 10:59, 18 June 2019
• Introductory stuff
  ...[prime]] number that is one less than a [[power of two]]. For example, 3 = 4 - 1 = 2² - 1 is a Mersenne prime; so is 7 = 8 - 1 = 2<sup>3</sup
  14 KB (2,370 words) - 15:15, 17 August 2019
• Triangular number
  :4△ = 4 + 3 + 2 + 1 = 10 (10 pin bowling uses a triangular arrangement.) :5△ = 5 + 4 + 3 + 2 + 1 = 15 (a common billiards arrangement is 15 balls in a triangle.
  655 bytes (81 words) - 12:49, 25 March 2019
• Square (geometry)
  A '''square''' is a regular polygon with 4 sides of equal length and with 4 equal interior angles (90 degrees), thus having opposing sides parallel. A square is the most constrained of all types of 4 sided figures.
  296 bytes (42 words) - 13:44, 18 September 2022
• Pocklington's theorem
  ...the [[KonyaginPomerance|Konyagin-Pomerance Test]] can be used. If <math>f^4 > n</math>, there is a polynomial-time algorithm, due to Coppersmith and Ho ...simplest one which will work for the value of ''f'' you have. For <math>f^4 < n</math>, there is no known algorithm which enhances Pocklington's theore
  2 KB (346 words) - 19:51, 30 August 2019
• Multiple polynomial quadratic sieve
  :<math>45^2\,\equiv \,2^4*7^0*13^1</math>
  6 KB (1,068 words) - 14:33, 13 February 2019
• How to get started with GIMPS
  ==Step 4==
  4 KB (623 words) - 13:39, 26 March 2019
• GIMPS networking, PrimeNet and communication
  Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
  8 KB (1,269 words) - 10:09, 7 March 2019
• Strong law of small numbers
  ...numbers. [[Double Mersenne number]]s are a good example of this. The first 4 terms yield primes, but factors for next four terms have been found (after
  1 KB (197 words) - 15:02, 11 February 2019
• P+1 factorization method
  If we define <math>D = u^2 - 4</math>, then for any odd prime <math>p</math>, <math>p</math> divides both
  8 KB (1,536 words) - 11:35, 12 February 2019
• SNFS polynomial selection
  ...lo ''N'', the number to be factored. Typically one polynomial is of degree 4, 5 or 6 (the algebraic side) and the other one is linear (the rational side 4. For <math>a^{11k}-1</math> and <math>a^{13k}-1</math> you'd get degrees 10
  7 KB (1,238 words) - 16:14, 12 February 2019
• ECMclient
  4. Run ecmclient.exe and it should get some work and start working on it.
  2 KB (383 words) - 11:16, 26 February 2019
• GMP-ECM
  ....1.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). 4. Time to open MSYS again. Inside MSYS you'll need to do as shown on this sc
  4 KB (567 words) - 10:54, 6 December 2019
• Gerbicz error checking
  *in [[Prime95]] since version 29.4 ...ot hold, then we roll back to the last stored <math>u</math> value (value (4) above). If we roll back too much (e.g. 100 times to the same term), then w
  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
  ...[exponent]]s of the [[Mersenne number]]s by ranges. It is broken down into 4 sets of vertical columns. The exponents below {{Num|10000000}} are treated
  7 KB (1,073 words) - 08:46, 15 May 2024
• Square number
  ...square integers is also a square number (e.g. 2/3&nbsp;&times;&nbsp;2/3 = 4/9). :2² = 4
  3 KB (408 words) - 13:56, 19 February 2019
• Riesel problem 1
  | 4 || 7 || {{Num|155274}} || {{Num|{{PAGESINCATEGORY:Riesel 2 1Intervals2|page ! scope="row" | [[:Category:Riesel 2 1Intervals4|4]]
  6 KB (689 words) - 18:14, 4 April 2024
• Mersenne.ca
  ...most efficient type of work for their particular CPU. Multiple CPUs (up to 4) can be compared directly to show relative efficiency comparison on all wor
  9 KB (1,396 words) - 15:42, 25 February 2019
• Aurifeuillian factor
  **<math>t\equiv 1 \pmod 4</math> and <math>n\equiv t \pmod{2t}</math> **<math>t\equiv 2, 3 \pmod 4</math> and <math>n\equiv 2t \pmod{4t}</math>
  10 KB (1,257 words) - 08:04, 24 June 2019
• Carol-Kynea prime 4
  |CKBase=4
  389 bytes (47 words) - 10:31, 10 June 2019
• Carol-Kynea prime
  ...integer. However these form a subset of another base’s primes (ex. Base 4 Carol/Kynea primes are Base 2 Carol/Kynea primes where <math>n \bmod 2 \equ
  8 KB (1,172 words) - 00:38, 6 July 2023
• Multifactorial number
  :<math>n!! = (n) \cdot (n-2) \cdot (n-4) \cdots</math>
  560 bytes (81 words) - 14:36, 20 July 2021
• Riesel prime 2 1
  2;T:ST;C:'''[[M1]]''', {{NWo|+|1}}, {{NWo|-|2}}, {{NWo|4|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
  2;T:ST;C:{{NWo|+|2}}, {{NWi|MM|4|1}} 4;C:{{NWo|-|4}}, {{NWi|MM|4|2}}
  5 KB (523 words) - 09:47, 5 October 2023
• Riesel prime 2 5
  4;C:{{NWo|+|4}}
  2 KB (196 words) - 18:36, 9 October 2021
• Riesel prime 2 15
  4;T:ST
  2 KB (252 words) - 13:29, 5 May 2024
• Riesel prime 2 2145
  4;T:S
  3 KB (329 words) - 07:59, 17 August 2021

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