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  • In [[mathematics]], a '''Fermat number''', named after [[Pierre de Fermat]] who first studied them, is a positive integer of the form where {{Vn}} is a [[non-negative]] [[integer]]. The first eight Fermat numbers are (see {{OEIS|l|A000215}}):
    12 KB (1,913 words) - 14:35, 9 August 2021
  • ...the form <math>b^n\pm 1</math> for <math>b</math> = 2, 3, 5, 6, 7, 10, 11, 12. The values of the exponent <math>n</math> are selected so there is never t ...it is considered the oldest continuously ongoing activity in computational number theory.
    7 KB (1,150 words) - 23:48, 19 April 2023
  • There are different kinds of '''generalized [[Fermat number]]s'''. :<math>F_{0,r}</math> generates the [[Mersenne number]]s.
    5 KB (726 words) - 09:57, 12 September 2021
  • 11;T:G ...}}<br>For all even {{Vn}}-values {{Kbn|+|9|2|n}} is a [[Generalized Fermat number]].
    3 KB (432 words) - 18:48, 9 April 2023
  • ...] of the form {{Kbn|+|k|b|n}} for 2 ≤ ''b'' ≤ 1030 and 2 ≤ ''k'' ≤ 12. {{HistF|2023-10-20|&nbsp;{{T5000|136544|{{Kbn|+|12|978|312346}}}}|Predrag Kurtovic|641052}}
    7 KB (789 words) - 11:31, 26 October 2023
  • Sequences (per base, {{Vk}}-value or individual number) with own page in this Wiki: | [[:Category:Mersenne prime|Mersenne primes]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Mersenne prime
    11 KB (1,385 words) - 17:23, 5 April 2024
  • ...}}<br>For all even {{Vn}}-values {{Kbn|+|4|3|n}} is a [[Generalized Fermat number]]. {{HistC|2019-12-07|1200000|Matthias Baur}}
    1 KB (120 words) - 21:11, 1 August 2021
  • 12;T:G |PRemarks=All values are [[Generalized Fermat number]]s.
    1 KB (112 words) - 19:02, 9 April 2023
  • ...arks=For all even {{Vn}}-values {{Kbn|+|25|2|n}} is a [[Generalized Fermat number]]. {{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
    2 KB (301 words) - 00:37, 9 March 2023
  • {{Generalized Fermat number |GFNa=12
    131 bytes (12 words) - 01:43, 31 July 2021
  • {{DISPLAYTITLE:Fermat numbers}} Factorizations and statistics of [[Fermat number]]s {{V|F}}<sub>{{V|m}}</sub> = {{Kbn|+|1|2|2<sup>m</sup>}} and their factor
    2 KB (252 words) - 22:50, 10 September 2021
  • {{DISPLAYTITLE:Generalized Fermat numbers 3<sup>2<sup>n</sup></sup>+1 div 2}} Factorizations and statistics of [[Generalized Fermat number]]s {{V|GF}}<sub>(3,1)</sub> = 3<sup>2<sup>n</sup></sup>+1 div 2 and their f
    2 KB (261 words) - 22:53, 10 September 2021
  • {{Generalized Fermat number |GFNa=12
    124 bytes (12 words) - 07:06, 24 August 2021
  • {{Generalized Fermat number |GFNn=11
    173 bytes (13 words) - 15:19, 27 August 2021
  • {{Generalized Fermat number |GFNa=12
    133 bytes (12 words) - 15:23, 30 August 2021
  • ...[Generalized Fermat number#Special conditions for Proth primes|Generalized Fermat primes]]. {{HistF|2012-01-11|1317378|Tim Rickard,PrimeGrid Proth Prime Search}}
    1 KB (127 words) - 10:01, 21 September 2021