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• Multiple polynomial quadratic sieve
  ...v u\,\pmod N</math> where <math>u</math> is the product of small [[prime]] numbers. The set of these primes is the ''factor base''. These relations will be fo ...ecause the logarithms are rounded and we do not sieve with powers of prime numbers), perform a trial division of <math>g_{a,b}(x)/a</math> by the elements of
  6 KB (1,068 words) - 14:33, 13 February 2019
• Proth number
  ...^{{Vn}} > {{Vk}}, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too. ...nd [[Fermat number]]s ({{Kbn|+|2ⁿ}}) are special forms of Proth numbers.
  670 bytes (104 words) - 10:59, 9 July 2021
• 27121 Search
  ...meGrid]], is a [[Distributed computing]] project, which searches for prime numbers of the form: 27 &times; 2ⁿ ± 1 and 121 &times; 2ⁿ ±
  983 bytes (138 words) - 13:25, 8 February 2019
• GIMPS chances of finding a prime number
  How does this apply to finding [[prime]] numbers? ...there isn't a single prime between 31,397 and 31,469, a gap of seventy-one numbers. But this thinning out does not happen evenly like a river broadening as it
  3 KB (593 words) - 10:09, 7 March 2019
• Bit level
  1 KB (193 words) - 18:47, 14 December 2023
• Strong law of small numbers
  ...athematician]] Richard K. Guy published a paper ''"The Strong Law of Small Numbers"''. In it he states, :"There aren't enough small numbers to meet the many demands made of them."
  1 KB (197 words) - 15:02, 11 February 2019
• P+1 factorization method
  ...ent the value <math>M</math> in binary form. Then erase the first "1" (all numbers when represented in binary start with the digit "1"). Then for every "1" wr
  8 KB (1,536 words) - 11:35, 12 February 2019
• General number field sieve
  ...most efficient classical [[Factorization|factoring method]] for 100+ digit numbers.}}
  478 bytes (59 words) - 12:04, 19 February 2019
• SNFS polynomial selection
  ==Cyclotomic numbers== For cyclotomic numbers, there are four standard operations you can perform on the number to derive
  7 KB (1,238 words) - 16:14, 12 February 2019
• NFSNET
  ...er field sieve|SNFS]] [[factorization]] methods to completely factor large numbers of interest to the math community. This project is now dead and replaced by ...zation]]s completed by NFSNET, all of them [[Cunningham project|Cunningham numbers]], are summarized below.
  4 KB (237 words) - 12:17, 13 February 2019
• Mersenneplustwo factorizations
  ...a prime, as well as simultaneously 2^p-1 being prime). All such numbers are divisible by 3 since 2^p-1 is not divisible by 3 (it's assume Participants use [[ECMclient]] to automatically download numbers, do ECM curves on them and upload them again.
  2 KB (215 words) - 13:33, 5 March 2019
• ECMclient
  ...al projects make use of ECMclient in their factoring of different kinds of numbers, including:
  2 KB (383 words) - 11:16, 26 February 2019
• GMP-ECM
  '''GMP-ECM''' is a program capable of factoring numbers using the [[Elliptic curve method|ECM]], [[P-1 factorization method|p-1]] a
  4 KB (567 words) - 03:05, 25 August 2024
• Gerbicz error checking
  ...um.org/showthread.php?t=22510 Original proposal of the technique for Proth numbers] ...hread.php?t=22471&p=465431 Original proposal of the technique for Mersenne numbers]
  3 KB (528 words) - 14:59, 3 October 2023
• MPZ APR-CL
  ...ed on systems that support 64-bit data type. It can prove the primality of numbers up to 6021 digits long. ...systems that only support 32-bit data type. It can prove the primality of numbers up to 3827 digits long.
  1 KB (226 words) - 19:44, 14 February 2019
• ECPP-DJ
  ...plementation of ECPP test. However, Primo runs much faster for 1000+ digit numbers, especially on multi-core machines (ECPP-DJ is single threaded).
  2 KB (237 words) - 18:04, 2 December 2019
• GIMPS PrimeNet reports
  Details known factors of Mersenne numbers However, if a Mersenne number has been fully factored the largest factor is Displays the results of the PRP tests on cofactors of Mersenne numbers. Information shown here is similar to that shown on the PRP Results report,
  7 KB (1,137 words) - 15:30, 13 August 2020
• 15k Search
  ...o the rate at which Proth/PRP/PFGW can perform a [[primality test]] on the numbers. Actually, you should stop a little sooner - the idea is to find primes, af
  3 KB (517 words) - 14:51, 15 February 2019
• On-Line Encyclopedia of Integer Sequences
  ...equence, the Encyclopedia search engine shows all sequences that match the numbers entered by the user. It can also find sequences given some text.
  582 bytes (87 words) - 15:31, 25 July 2020
• Milestones report
  *[[Double check]]ing all numbers less than a given Mersenne Prime, thus proving its place in the sequence of *Testing all numbers less than a given Mersenne Prime once.
  2 KB (298 words) - 12:39, 19 February 2019

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