Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Search results

Jump to: navigation, search

Create the page "K,n-pair" on this wiki! See also the search results found.

  • Mersenne prime
    ...2}</math>, where <math>S_0=4</math> and for <math>k>0</math>, <math>S_k=S_{k-1}^2-2</math>. * [[Riesel prime 2 1|Riesel primes for k=1]]
    5 KB (857 words) - 14:53, 19 September 2021
  • Fermat number
    *'''[[Proth's theorem]]''' -- (1878) Let {{V|N}} = {{Kbn|+|k|2|m}} with odd {{Vk}} < 2<sup>{{V|m}}</sup>. If there is an integer {{V|a}} ...des <math>S_{2^n-2}</math> where <math>S_0=5</math> and <math>S_{k+1}=S^2_{k}-2</math> ([http://www.robertgerbicz.tar.hu/Fermatnumbers.pdf Proof] by Rob
    12 KB (1,913 words) - 14:35, 9 August 2021
  • Cunningham project
    :<math>(b^{kn}-1) = (b^n-1) \sum _{r=0}^{k-1} b^{rn}</math> for any value of <math>k</math> and
    7 KB (1,150 words) - 23:48, 19 April 2023
  • Lucas-Lehmer test
    ...ath>\omega</math> to get that <math>\omega^{k-j}=1</math>, with <math>1\le k-j\le F^2-1</math>. We have proven that <math>\omega</math> satisfies <math Any number of the form <math>I_k=\omega^k + \bar\omega^k</math>, where <math>k</math> is positive odd integer, can be used as an initial value <math>S_0</
    20 KB (3,572 words) - 14:30, 17 February 2019
  • Conjectures 'R Us
    For every base ({{Vb}} &le; 1030) for the forms {{Kbn|±|k|b|n}} there is a {{Vk}}-value for each form that has been conjectured to be Assist in proving the [[Liskovets-Gallot conjectures]] for the forms {{Kbn|±|k|2|n}} where {{Vn}} is always odd '''and''' where {{Vn}} is always even.
    3 KB (503 words) - 02:20, 1 May 2024
  • Fast Fourier transform
    :<math>\large f_j = \sum_{k=0}^{n-1} x_k e^{-{2\pi i \over n} jk } \qquad j = 0, ... ,n-1.</math> ...Tukey FFTs, for example), via the identity <math>jk = -(j-k)^2/2 + j^2/2 + k^2/2</math>.
    17 KB (2,684 words) - 18:50, 28 September 2023
  • No Prime Left Behind
    ...n 2008-01-10. The project searches for [[Riesel prime]]s of the form {{Kbn|k|2|n}} with odd {{Vk}} and 300 < {{Vk}} < 1001 and {{Vn}} > 260000 not reser
    745 bytes (111 words) - 02:17, 1 May 2024
  • Rational number
    :<math>\large a + \frac{k(b-a)}{n+1}</math> by varying the number <math>k</math> from 1 to <math>n</math>. Then we can make the value <math>n</math>
    3 KB (541 words) - 15:01, 26 March 2023
  • Modular arithmetic
    ...>2^m</math>, let the number to be inverted be <math>N</math> and let <math>k = \log_2 m</math> rounded to the next integer. Then the method is: # Perform k times: Set x = x(2-Nx) mod 2^m
    4 KB (625 words) - 10:25, 23 January 2019
  • Montgomery multiplication
    ...] \,+\, a'[1] * 2^k \,+\, a'[2] * 2^{2k} \,+\, ... \,+\, a'[s-1] * 2^{(s-1)k}</math>. and similarly for b' and c'. The number <math>k</math> is the number of bits of the integer, and <math>n = ks</math>.
    4 KB (582 words) - 17:01, 29 August 2022
  • Elliptic curve method
    ...ion does not change by multiplying all coordinates by the same value <math>k\neq 0</math>. ...y using another point. When we compute k'''P''' we will be also computing (k+1)'''P'''.
    19 KB (3,181 words) - 22:27, 6 July 2023
  • Wacław Sierpiński
    ...ntegers {{Vk}} (named [[Sierpiński number]]s after him) such that {{Kbn|+|k|n}} is composite for all {{Vn}}.
    592 bytes (86 words) - 00:38, 15 January 2024
  • Sierpiński number
    ...ierpiński number''' is an odd natural number {{Vk}} such that all {{Kbn|+|k|n}} for all {{Vn}} are [[Composite number|composite]].
    324 bytes (48 words) - 13:37, 8 April 2023
  • Sierpiński problem
    Consider numbers of the form {{V|N}} = {{Kbn|+|k|n}}, where {{Vk}} is odd and {{Vn}} > 0. If, for some fixed {{Vk}}, every i
    5 KB (650 words) - 10:25, 26 March 2024
  • Seventeen or Bust
    |result=11 k's eliminated as a standalone project, 1 k eliminated as a subproject on PrimeGrid ...he project is to find [[prime]]s of the form <math>k*2^n+1</math>, where ''k'' is one of the remaining 17 (now 5) candidates for [[Sierpiński number]]s
    3 KB (544 words) - 16:44, 21 July 2019
  • Perfect number
    :where ''q'', ''p''<sub>1</sub>, &hellip;, ''p''<sub>''k''</sub> are distinct primes and ''q'' &equiv; &alpha; &equiv; 1 (mod 4) (Eu
    6 KB (885 words) - 11:33, 7 March 2019
  • Mfaktc
    *[[Factor]] sizes <math><2^{95}</math> and '''[[value k]]''' <math><2^{63.9}</math>
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    ...ssSize: defines how far many bits of the sieve each TF block processes (in K bits). Larger values may lead to less wasted cycles by reducing the number
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Riesel number
    A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s.
    827 bytes (112 words) - 08:21, 25 March 2024
  • Primality test
    *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}}, making it useful in several [[distrib
    3 KB (501 words) - 05:20, 3 August 2021
  • Primality testing program
    | k &times; b<sup>n</sup>±c general numbers | k &times; b<sup>n</sup>±c
    2 KB (314 words) - 21:23, 29 August 2019
  • Pépin's test
    ...t 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
    :<math>\sum_{k=1}^{n}\,(2k-1)\,=\,n^{2}</math> ::<math>\sum_{k=1}^{1}\,(2k-1)\,=\,2-1\,=\,1^{2}</math>
    4 KB (679 words) - 13:57, 20 February 2019
  • GIMPS factoring and sieving
    ...e of the algebraic form <math>2kp+1</math> for some positive integer <math>k</math> and furthermore must also leave a remainder of either 1 or 7 upon di
    6 KB (962 words) - 10:08, 7 March 2019
  • LLR
    **[[Lucas-Lehmer-Riesel algorithm]] for {{Kbn|k|n}} numbers. **[[Proth's theorem|Proth algorithm]] for {{Kbn|+|k|n}} numbers.
    2 KB (300 words) - 22:00, 16 December 2023
  • P-1 factorization method
    ...1</math>, where ''k'' is a non-negative integer. This means that <math>a^{k(p-1)} - 1</math>
    5 KB (814 words) - 01:35, 12 March 2019
  • Self-initializing quadratic sieve
    ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln1} + k*p</math> of the sieve array. ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln2} + k*p</math> of the sieve array.
    10 KB (1,763 words) - 02:56, 12 March 2019
  • Miller-Rabin pseudoprimality test
    ...er being tested for primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number. Then consider the sequence <math>a^k</math>, <math>a^{2k}</math>, <math>a^{4k}</math>..., <math>a^{N-1}</math> m
    3 KB (432 words) - 15:33, 28 January 2019
  • Generalized Fermat number
    ...F_{n,2}</math> numbers can be proven prime by using [[Pépin's test]] with k=5. ...[[Generalized Fermat number]]s for any [[Proth prime|Proth primes {{Kbn|+|k|n}}]] are listed as ''GF Divisor'' on their own page. They are listed as ''
    5 KB (726 words) - 09:57, 12 September 2021
  • PrimeGrid
    ...rime Search|Proth Prime Search]]: searching for primes of the form {{Kbn|+|k|2|n}}. ...ed|Proth Prime Search Extended]]: searching for primes of the form {{Kbn|+|k|2|n}}.
    3 KB (458 words) - 10:28, 26 March 2024
  • Sieve of Eratosthenes
    *First, list out all the integers <math>1 \leq k \leq N</math>. ...ssary because all composite numbers <math>11 \geq \sqrt{N} = 10 \geq \sqrt{k}</math> have already been crossed out.
    4 KB (654 words) - 11:10, 6 February 2019
  • Twin Prime Search
    ...t that looks for large [[twin prime]]s ([[Riesel prime|Riesel type]] {{Kbn|k|n}}) of world record size.
    826 bytes (100 words) - 11:04, 21 March 2024
  • Riesel Prime Search
    :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1.
    845 bytes (120 words) - 02:21, 1 May 2024
  • Seventeen or Bust/Factoring
    factor | k*2^n+1
    3 KB (491 words) - 13:39, 1 February 2019
  • Seventeen or Bust/PRP
    ==Working on the k,n pair==
    888 bytes (145 words) - 13:40, 1 February 2019
  • Sieving
    ...ts of the array <math>k</math>, <math>k+p</math>, <math>k+2p</math>, <math>k+3p</math>, and so on correspond to multiples of the prime.
    3 KB (521 words) - 11:14, 6 February 2019
  • Sieving program
    ...of numbers of the form K &times; 2<sup>n</sup> + 1 or - 1. Independent of K's, but good for many N's too) and [[TPSieve]] (similar to PPSieve, but for *[[TwinGen]] (performing sieving of numbers of the form k&times;2<sup>n</sup>+/-1) http://www.underbakke.com/primes/
    2 KB (220 words) - 11:42, 7 March 2019
  • NewPGen
    *k&times;b<sup>n</sup>+1 *k&times;b<sup>n</sup>-1
    3 KB (529 words) - 09:32, 7 March 2019
  • Proth's theorem
    Let <math>p = k*2^n+1</math> and <math>k < 2^n</math>; then <math>p</math> is prime if there is an integer <math>a</
    549 bytes (88 words) - 18:15, 28 September 2023
  • Proth prime
    ...f numbers, but primes in the form {{Kbn|+|k|n}} with 2<sup>''n''</sup> > ''k'' are often called Proth primes. *[[Proth prime table|Table]] with all available ''k''-values
    656 bytes (91 words) - 07:02, 31 August 2020
  • Riesel prime
    ...ial definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}} are called like this on many pages. ...mersenneforum.org/showthread.php?t=29635 "Team drive #1 for {{Vk}}<300: 26 k's for {{Vn}}>2M"]: [https://www.mersenneforum.org/showpost.php?p=655608 #1
    2 KB (279 words) - 03:48, 24 April 2024
  • Pocklington's theorem
    :Let <math>N-1 = q^k\,R</math> where ''q'' is a prime which does not divide ''R''. If there is a
    2 KB (346 words) - 19:51, 30 August 2019
  • Multiple polynomial quadratic sieve
    ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln1} + k*p</math> of the sieve array. ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln2} + k*p</math> of the sieve array.
    6 KB (1,068 words) - 14:33, 13 February 2019
  • Proth number
    :{{V|N}} = {{Kbn|+|k|2|n}}
    670 bytes (104 words) - 10:59, 9 July 2021
  • Worktodo.txt
    *[[PRP]]=k,b,n,c<nowiki>[</nowiki>,how_far_factored,tests_saved<nowiki>][</nowiki>,kno *Pfactor=assignment ID,[[value k|k]],b ([[base]]),n ([[exponent]]),c,how far factored,[[Lucas-Lehmer test|LL]]
    2 KB (273 words) - 22:58, 11 May 2019
  • P+1 factorization method
    ...e. When we compute <math>V_{kn}</math> we will be also computing <math>V_{(k+1)n}</math>. ...d when the bit equals one we compute (<math>V_{(2k+1)n}</math>, <math>V_{2(k+1)n}</math>). In both cases we need one duplication and one addition requir
    8 KB (1,536 words) - 11:35, 12 February 2019
  • SNFS polynomial selection
    ...-1)} + a\cdot a^{k-1} + 1</math> and can convert to a quartic in <math>a^{(k-1)/2}</math>. If you want a sextic, tweak the exponents accordingly by 2., ...+ a^{3k} + a^{2k} + a^k + 1</math>, which is a useable quartic in <math>a^k</math>.
    7 KB (1,238 words) - 16:14, 12 February 2019
  • Gerbicz error checking
    Let <math>p</math> be a Proth number, and let <math>k</math>, <math>n</math>, and <math>a</math> be defined as on [[Proth's theor # <math>u(t) \equiv (a^k)^{2^t} \pmod{p}</math>
    3 KB (528 words) - 14:59, 3 October 2023
  • 15k Search
    :This was the initial phase, to gather information about heavy k, for later use with fixed n forms. :Fixed n searches are faster than fixed k, and can be used in conjunction with heavy 15k.
    3 KB (517 words) - 14:51, 15 February 2019
  • Sierpiński number base 5
    A '''Sierpiński number base 5''' is a value of {{Vk}} such that {{Kbn|+|k|5|n}} is always [[composite number|composite]].
    556 bytes (83 words) - 10:57, 14 October 2020
  • Riesel number base 5
    A '''Riesel number base 5''' is a value of ''k'' such that {{Kbn|-|k|5|n}} is always a [[composite number]].
    589 bytes (90 words) - 10:30, 26 March 2024
  • Riesel problem 1
    {{DISPLAYTITLE:Riesel problem, {{Kbn|-|k|2|n}}, {{Vk}} < {{Num|509203}}}} ...howed that there are an infinite number of integers {{Vk}} such that {{Kbn|k|2|n}} is not prime for any integer {{Vn}}. He showed that the number {{Vk}}
    6 KB (689 words) - 18:14, 4 April 2024
  • Tutorial LLR
    #Move the .txt-file from NewPGen, containing the k/n combinations you wish to test, to the same folder as LLR ...Make sure the numbers are of the same form (normally k*2<sup>n</sup>+1 or k*2<sup>n</sup>-1).
    2 KB (337 words) - 13:24, 20 February 2019
  • Aurifeuillian factor
    ::<math>2^{4k+2}+1 = (2^{2k+1}-2^{k+1}+1)\cdot (2^{2k+1}+2^{k+1}+1)</math> |2<sup>4''k'' + 2</sup> + 1
    10 KB (1,257 words) - 08:04, 24 June 2019
  • Mtsieve
    ...the form {{Kbn|+|k|b|n}} and {{Kbn|k|b|n}} for fixed b and n and variable k *fkbnsieve: search for factors of the form k*b<sup>n</sup>+c for fixed k, b, and n and variable c
    2 KB (338 words) - 06:58, 28 March 2023
  • Carol-Kynea prime
    ...are also classified as near-square numbers (numbers of the form <math>n^2-k</math>). ...ynea_prime_remaining.csv|format=csv with header|delimiter=;|data=b=b,C=C,K=K}}
    8 KB (1,172 words) - 00:38, 6 July 2023
  • Riesel 2 Low-weight
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with Nash weight < 1000}} Riesel numbers {{Kbn|k|n}} where the [[Nash weight]] is smaller than 1000.
    948 bytes (121 words) - 13:08, 21 July 2021
  • Proth prime table
    ...="width:4em; background:PaleGreen; display:inline-block;">&nbsp;</div> : ''k''-value is reserved ...le="width:4em; background:#F8F9FA; display:inline-block;">&nbsp;</div> : ''k''-value is not reserved
    750 bytes (108 words) - 14:39, 12 July 2021
  • Williams prime PM 10
    ...br>See history at Studio Kamada [https://stdkmd.net/nrr/prime/prime_m1.htm k*10^n-1 form] and [https://stdkmd.net/nrr/prime/prime_difficulty.txt difficu
    953 bytes (108 words) - 18:12, 21 April 2024
  • Riesel prime small bases least n
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|b|n}}, least {{Vn}}-values}} ...wn 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}} &le; 12.
    6 KB (684 words) - 09:40, 17 March 2024
  • Proth prime small bases least n
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|b|n}}, least ''n''-values}} ...h prime]] of the form {{Kbn|+|k|b|n}} for 2 ≤ ''b'' ≤ 1030 and 2 ≤ ''k'' ≤ 12.
    7 KB (795 words) - 08:03, 5 May 2024
  • Proth.exe
    * {{Kbn|+|1|k|n}} ([[Generalized Fermat number]]s) * {{Kbn|±|k|b|n}} (by default {{Vb}} is 2 but it can be changed)
    667 bytes (101 words) - 16:44, 31 August 2021
  • Twin prime least k
    {{DISPLAYTITLE: Twin primes of the form {{Kbn|k|n}} and {{Kbn|+|k|n}}, least {{Vk}} value}} ...ues ≥ 1 for any 1 ≤ {{Vn}} ≤ 16999 such that {{Kbn|k|n}} and {{Kbn|+|k|n}} are simultaneously prime, which means they form a set of [[twin prime]]
    993 bytes (142 words) - 09:00, 28 May 2021
  • RPS Drive 10
    *Purpose: The goal of this drive is to search for primes of the form '''{{Kbn|k|n}}''' for '''128 low-weighted {{Vk}}'s with 10000 < {{Vk}} < 35000'''.
    2 KB (290 words) - 22:54, 10 April 2024
  • Riesel 2 1-300
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Vk}} < 300}}
    855 bytes (117 words) - 07:27, 16 July 2021
  • RPS Megabit Drive 1
    The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1000000.
    4 KB (439 words) - 10:45, 9 May 2024
  • RPS Megabit Drive 2
    The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1000000.
    4 KB (376 words) - 21:41, 8 May 2024
  • RPS Megabit Drive 3
    The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1400000.
    2 KB (155 words) - 07:18, 7 May 2024
  • Riesel 2 10e4-10e5
    __NOTOC__{{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Num|10000}} &le; {{Vk}} &le; {{Num|25000}}}}
    1 KB (176 words) - 09:20, 22 July 2021
  • Riesel 2 4000-6000
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 4000 < {{Vk}} < 6000}}
    883 bytes (117 words) - 08:42, 22 July 2021
  • Riesel 2 300-2000
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 300 < {{Vk}} < 2000}}
    878 bytes (117 words) - 08:27, 22 July 2021
  • RPS Drive 7
    *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|n}} for 21 high-weighted 2200 < {{Vk}} < 3000.
    1 KB (123 words) - 03:03, 17 April 2024
  • Riesel 2 10e5-10e6
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10<sup>5</sup> < {{Vk}} < 10<sup>6</sup>}}
    1 KB (153 words) - 09:34, 22 July 2021
  • Riesel 2 10e6-10e7
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10<sup>6</sup> < {{Vk}} < 10<sup>7</sup>}}
    1 KB (153 words) - 09:46, 22 July 2021
  • Riesel 2 10e7-10e8
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10<sup>7</sup> < {{Vk}} < 10<sup>8</sup>}}
    1 KB (153 words) - 09:58, 22 July 2021
  • Riesel 2 10e8-10e9
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10<sup>8</sup> < {{Vk}} < 10<sup>9</sup>}}
    1 KB (153 words) - 10:00, 22 July 2021
  • Riesel 2 10e9-10e10
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10<sup>9</sup> < {{Vk}} < 10<sup>10</sup>}}
    1 KB (153 words) - 10:05, 22 July 2021
  • NPLB Drive 9
    ...drive #9 for NPLB. We will be searching all k=1005-2000 for n=50K-200K and k=1400-2000 for n=200K-350K.
    383 bytes (55 words) - 12:28, 13 June 2020
  • NPLB Drive 10
    This is team drive #10 for No Prime Left Behind. We will be searching all k=1400-2000 for n=500K-1M.
    402 bytes (56 words) - 11:55, 5 September 2021
  • NPLB Drive 12
    This is team drive #12 for NPLB. We will be searching all k=2000-3000 for n=50K-425K.
    353 bytes (48 words) - 12:32, 13 June 2020
  • PrimeGrid Sophie Germain Search
    ...he project searched for prime numbers of the form {{Kbn|k|1290000}}, for ''k'' ≤ 10<sup>13</sup>. ...Kbn|k|1290001}} or {{Kbn|k|1289999}}, and Twin pairs take the form {{Kbn|+|k|1290000}}.<ref>[https://www.primegrid.com/forum_thread.php?id=1450&nowrap=t
    3 KB (337 words) - 15:13, 16 December 2023
  • Riesel 2 2000-4000
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 2000 < {{Vk}} < 4000}}
    883 bytes (117 words) - 08:39, 22 July 2021
  • Riesel 2 6000-8000
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 6000 < {{Vk}} < 8000}}
    883 bytes (117 words) - 08:56, 22 July 2021
  • Riesel 2 8000-10000
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 8000 < {{Vk}} < 10000}}
    888 bytes (117 words) - 09:00, 22 July 2021
  • Riesel 2 10e10-infinity
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Vk}} > 10<sup>10</sup>}}
    1 KB (146 words) - 10:08, 22 July 2021
  • RPS Drive 9
    *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|n}} for 40 high-weighted 10000 < {{Vk}} < 30000.
    2 KB (151 words) - 10:56, 11 January 2023
  • Riesel 2 Riesel
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}}}} '''Riesel numbers''' are odd numbers {{Vk}} for which {{Kbn|k|n}} is composite for all natural numbers {{Vn}}.
    808 bytes (110 words) - 21:12, 17 December 2023
  • Riesel 2 Count-100
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with 100 and more primes}} Riesel numbers {{Kbn|k|n}} with 100 or more prime values {{Vn}}.
    911 bytes (120 words) - 21:56, 25 July 2021
  • Riesel 2 15k-value
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 15 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 15.
    1 KB (156 words) - 06:59, 16 July 2021
  • Riesel 2 2145k-value
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 2145 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 2145.
    1 KB (156 words) - 07:01, 16 July 2021
  • Riesel 2 2805k-value
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 2805 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 2805.
    1 KB (156 words) - 07:08, 16 July 2021
  • Riesel 2 Count-0
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with no prime value so far}} Riesel numbers {{Kbn|k|n}} where no prime values are known.
    871 bytes (117 words) - 21:46, 25 March 2024
  • Liskovets-Gallot conjectures
    [[Valery Liskovets]] studied the list of {{Kbn|+|k|n}} primes and observed, that the {{Vk}}'s ({{Vk}} divisible by 3) <blockquote>'''There exist {{Vk}}, 3|{{Vk}}, such that primes {{Kbn|+|k|n}} do exist but only with odd {{Vn}}/only with even {{Vn}}.'''</blockquote
    2 KB (367 words) - 12:42, 9 May 2024
  • CRUS Liskovets-Gallot
    ...ormat=csv with header|delimiter=,|data=date=date,mforum=mforum,user=user,k=k,n=n}} ...ign:right" data-sort-value={{{k}}} {{!}} [[Riesel prime 2 {{{k}}}|{{Kbn|{{{k}}}|{{{n}}}}}]]
    7 KB (957 words) - 22:40, 10 June 2023
  • Riesel prime 2 39939
    |RRemarks=This k-value seems the smallest k ≡ 0 mod 3 for which {{Kbn|k|n}} is never prime for an even ''n''. See [[Liskovets-Gallot conjectures]].
    443 bytes (43 words) - 08:19, 1 August 2021
  • Riesel prime 2 172677
    ...ks=This {{Vk}}-value seems the smallest {{Vk}} ≡ 0 mod 3 for which {{Kbn|k|n}} is never prime for an odd {{Vn}}. See [[Liskovets-Gallot conjectures]].
    383 bytes (44 words) - 12:53, 29 July 2021
  • Proth prime 2 66741
    ...proved in 2015 to be the smallest odd {{Vk}} ≡ 0 mod 3 for which {{Kbn|+|k|n}} is never prime for an even {{Vn}}. See [[Liskovets-Gallot conjectures]]
    396 bytes (50 words) - 09:17, 10 May 2024
  • Proth prime 2 95283
    ...=This {{Vk}}-value seems the smallest {{Vk}} ≡ 0 mod 3 for which {{Kbn|+|k|n}} is never prime for an odd {{Vn}}. See [[Liskovets-Gallot conjectures]].
    457 bytes (43 words) - 15:52, 11 July 2021
  • Nash weight
    ...ris Nash]] gave a weight to show the number of remaining values of {{Kbn|+|k|n}} after sieving the range 100000 < {{Vn}} < 110000 after performing a Nas A later definition was also done for {{Kbn|k|n}}.
    2 KB (330 words) - 09:11, 23 September 2021
  • Riesel 2 3k-value
    {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 3 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 3.
    1 KB (153 words) - 06:55, 16 July 2021
  • Riesel prime 10
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|10|n}}}} ...www.noprimeleftbehind.net/gary/primes-kx10n-1.htm Primes of the form {{Kbn|k|10|n}}] compiled by [[Gary Barnes]]
    681 bytes (93 words) - 13:01, 2 August 2021
  • Riesel 2 10e4-10e5a
    __NOTOC__{{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Num|25000}} &le; {{Vk}} &le; {{Num|100000}}}}
    1 KB (165 words) - 09:15, 22 July 2021
  • RPS Drive 12
    *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|2|n}} for 13 high-weighted 2000 < {{Vk}} < 2300. *k-values: 2043, 2049, 2061, 2079, 2085, 2103, 2127, 2205, 2211, 2253, 2259, 2
    537 bytes (60 words) - 10:53, 11 January 2023
  • Riesel 2 Missing-range
    {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}} with missing ranges}}
    1 KB (192 words) - 09:07, 23 September 2021
  • PrimeGrid Seventeen or Bust
    To solve the [[Sierpiński problem]] by finding a prime of the form {{Kbn|+|k|n}} for each remaining value of {{Vk}} < 78,557.
    1 KB (135 words) - 11:42, 5 September 2021
  • PrimeGrid Prime Sierpiński Problem
    ...{Vk}} < 271129 must be shown to produce a prime number of the form {{Kbn|+|k|n}}.
    2 KB (254 words) - 11:43, 5 September 2021
  • Proth 2 3k-value
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 3 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 3.
    1 KB (156 words) - 09:18, 23 July 2021
  • PrimeGrid New Sierpiński Problem
    ...like the [[Sierpiński problem]] but with first prime at <math>n > \log_2(k)</math>
    461 bytes (62 words) - 07:27, 25 January 2024
  • PrimeGrid Fermat Divisor Search
    The project searched for [[Fermat divisor]]s of the form {{Kbn|+|k|2|n}}, for the following ranges:<ref name="table"/>
    4 KB (448 words) - 09:13, 7 September 2021
  • Riesel problem 2
    {{DISPLAYTITLE:Riesel problem 2, {{Kbn|-|k|2|n}}, {{Num|509203}} < {{Vk}} < {{Num|762701}}}} ...esel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for 509203 &lt; {{Vk}} &lt; 762701, the first and second Riesel {{Vk}
    4 KB (386 words) - 06:41, 29 March 2024
  • Proth 2 15k-value
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 15 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 15.
    1 KB (156 words) - 09:22, 23 July 2021
  • Proth 2 2145k-value
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 2145 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 2145.
    1 KB (156 words) - 09:36, 23 July 2021
  • Proth 2 2805k-value
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with {{Vk}} mod 2805 = 0}} Proth numbers {{Kbn|+|k|n}} where {{Vk}}-value is a multiple of 2805.
    1 KB (158 words) - 09:16, 22 March 2024
  • Proth 2 1-300
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Vk}} < 300}}
    850 bytes (117 words) - 17:18, 25 July 2021
  • Proth 2 Sierpinski
    {{DISPLAYTITLE:Sierpiński numbers of the form {{Kbn|+|k|n}}}} '''Sierpiński numbers''' are odd numbers {{Vk}} for which {{Kbn|+|k|n}} is composite for all natural numbers {{Vn}}.
    741 bytes (99 words) - 21:18, 17 December 2023
  • Proth 2 Count-0
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with no prime value so far}} Proth numbers {{Kbn|+|k|n}} where no prime values are known.
    867 bytes (117 words) - 07:46, 26 July 2021
  • Proth 2 Count-100
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with 100 and more primes}} Proth numbers {{Kbn|+|k|n}} with 100 or more prime values {{Vn}}.
    916 bytes (122 words) - 07:51, 26 July 2021
  • Proth 2 Missing-range
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}} with missing ranges}}
    778 bytes (107 words) - 07:57, 26 July 2021
  • Proth 2 300-2000
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 300 < {{Vk}} < 2000}}
    873 bytes (117 words) - 08:15, 26 July 2021
  • Proth 2 2000-4000
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 2000 < {{Vk}} < 4000}}
    878 bytes (117 words) - 08:17, 26 July 2021
  • Proth 2 4000-6000
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 4000 < {{Vk}} < 6000}}
    887 bytes (118 words) - 08:18, 26 July 2021
  • Proth 2 6000-8000
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 6000 < {{Vk}} < 8000}}
    887 bytes (118 words) - 08:20, 26 July 2021
  • Proth 2 8000-10000
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 8000 < {{Vk}} < 10000}}
    883 bytes (117 words) - 08:21, 26 July 2021
  • Proth 2 10e4-10e5
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Num|10000}} &le; {{Vk}} &le; {{Num|100000}}}}
    1 KB (170 words) - 08:26, 26 July 2021
  • Proth 2 10e5-10e6
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>5</sup> < {{Vk}} < 10<sup>6</sup>}}
    1 KB (153 words) - 08:29, 26 July 2021
  • Proth 2 10e6-10e7
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>6</sup> < {{Vk}} < 10<sup>7</sup>}}
    1 KB (153 words) - 08:33, 26 July 2021
  • Proth 2 10e7-10e8
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>7</sup> < {{Vk}} < 10<sup>8</sup>}}
    1 KB (153 words) - 08:34, 26 July 2021
  • Proth 2 10e8-10e9
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|k|n}}, 10<sup>8</sup> < {{Vk}} < 10<sup>9</sup>}}
    1 KB (153 words) - 08:35, 26 July 2021
  • Proth 2 10e9-10e10
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, 10<sup>9</sup> < {{Vk}} < 10<sup>10</sup>}}
    1 KB (153 words) - 08:36, 26 July 2021
  • Proth 2 10e10-infinity
    {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|n}}, {{Vk}} > 10<sup>10</sup>}}
    1 KB (146 words) - 08:38, 26 July 2021
  • Generalized Fermat number 2 1
    ...<sub>{{V|m}}</sub> = {{Kbn|+|1|2|2<sup>m</sup>}} and their factors {{Kbn|+|k|2|n}}.
    2 KB (252 words) - 22:50, 10 September 2021
  • GF Divisors 2 1
    GF Divisors {{Kbn|+|k|2|n}} of [[Fermat number]]s {{V|F}}<sub>{{V|m}}</sub> = {{Kbn|+|1|2|2<sup>m
    595 bytes (83 words) - 22:51, 10 September 2021
  • Proth 2 Low-weight
    {{DISPLAYTITLE:Proth numbers of the form {{Kbn|+|k|n}} with Nash weight < 1000}} Proth numbers {{Kbn|+|k|n}} where the [[Nash weight]] is smaller than 1000.
    944 bytes (121 words) - 18:22, 5 August 2021
  • Generalized Fermat number 3 1
    ...>(3,1)</sub> = 3<sup>2<sup>n</sup></sup>+1 div 2 and their factors {{Kbn|+|k|2|n}}.
    2 KB (261 words) - 22:53, 10 September 2021
  • GF Divisors 3 1
    GF Divisors {{Kbn|+|k|2|n}} of [[Generalized Fermat number]]s {{V|GF}}<sub>(3,1)</sub> = 3<sup>2<
    617 bytes (84 words) - 22:54, 10 September 2021
  • PrimeGrid Proth Prime Search
    Finding primes in the form {{Kbn|+|k|n}} for the following {{Vk}} and {{Vn}}-ranges:
    1 KB (139 words) - 23:57, 13 May 2024
  • PrimeGrid Proth Prime Search Extended
    Finding primes for the form {{Kbn|+|k|n}} for 1200 < {{Vk}} < 10000 to {{Vn}}=3322000.
    490 bytes (61 words) - 11:42, 5 September 2021
  • PrimeGrid Proth Mega Prime Search
    Finding primes for the form {{Kbn|+|k|n}} for 1200 < {{Vk}} < 10000 to {{Vn}}=3600000.
    862 bytes (109 words) - 09:55, 21 October 2023
  • RPS Drive 11
    *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|2|n}} for 123 values with 2000 < {{Vk}} < 2300. *k-values: 123 values
    565 bytes (77 words) - 10:57, 11 January 2023
  • Fermat divisor
    ...divisor of a [[Fermat number]] {{V|F<sub>n</sub>}} is of the form {{Kbn|+|k|n+2}} (so a [[Proth prime]]).
    445 bytes (71 words) - 09:09, 7 September 2021
  • Riesel problem 3
    {{DISPLAYTITLE:Riesel problem 3, {{Kbn|-|k|2|n}}, {{Num|762701}} < {{Vk}} < {{Num|777149}}}} ...esel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for {{Num|762701}} &lt; {{Vk}} &lt; {{Num|777149}}, the second and th
    4 KB (337 words) - 18:52, 30 April 2024
  • Even Riesel Problem
    ...m]] is to find the smallest [[Riesel number]] {{Vk}} (odd) such that {{Kbn|k|2|n}} is composite for every {{Vn}} &ge; 1.<br> ...dingly there comes up a question: Is there any even {{Vk}} for which {{Kbn|k|2|n}} is never prime?
    7 KB (718 words) - 10:32, 26 March 2024
  • Twin Prime Search 480000
    ...h_480000.csv|format=csv with header|delimiter=,|data=date=date,user=user,k=k,n=n}} {{!}} style="text-align:right" {{!}} [[Riesel prime 2 {{{k}}}|{{Kbn|{{{k}}}|{{{n}}}}}]]
    2 KB (262 words) - 10:53, 21 March 2024
  • Riesel problem 4
    {{DISPLAYTITLE:Riesel problem 4, {{Kbn|-|k|2|n}}, {{Num|777149}} < {{Vk}} < {{Num|790841}}}} ...esel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for {{Num|777149}} &lt; {{Vk}} &lt; {{Num|790841}}, the third and fou
    4 KB (336 words) - 18:50, 30 April 2024
  • Riesel problem real 1
    {{DISPLAYTITLE:Real Riesel problem 1, {{Kbn|-|k|2|n}}, {{Vk}} < {{Num|509203}}, {{Vb}}<sup>{{Vn}}</sup> &gt; {{Vk}}}}
    938 bytes (122 words) - 12:25, 14 April 2024
  • Drive Data test
    *k-values: if ongoing, currently used values *n-range: like k-values
    4 KB (513 words) - 08:09, 15 May 2024
Retrieved from "https://www.rieselprime.de/ziki/Special:Search"