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

Difference between revisions of "Cullen number"

From Prime-Wiki
Jump to: navigation, search
(last update + all PP-links)
m
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Last update|2019-02-27}}
+
A '''Cullen number''' {{V|C<sub>n</sub>}} is a number of the form {{Kbn|+|n|2|n}},
A '''Cullen number ''C<sub>n</sub>'' ''' is a number of the form ''n'' &times; 2<sup>''n''</sup> + 1,<br />
+
 
a '''generalized Cullen number''' base ''b'' is a number of the form ''n'' &times; ''b''<sup>''n''</sup> + 1. '''(perhaps own page?)'''
+
a '''generalized Cullen number''' base {{Vb}} is a number of the form {{Kbn|+|n|b|n}}. '''(perhaps own page?)'''
  
 
==Cullen primes==
 
==Cullen primes==
''C<sub>n</sub>'' is [[prime]] for ''n'' = 1, 141, {{PP|40087|4713}}, {{PP|38112|5795}}, {{PP|37374|6611}}, {{PP|23436|18496}}, {{PP|17877|32292}}, {{PP|17850|32469}}, {{PP|10752|59656}}, {{PP|5931|90825}}, {{PP|271|262419}}, {{PP|102|361275}}, {{PP|77|481899}}, {{PP|75433|1354828}}, {{PP|87775|6328548}}, {{PP|89536|6679881}} and for no other ''n'' < {{Num|17200000}} ({{OEIS|l|A005849}}).
+
{{V|C<sub>n</sub>}} is [[prime]] for {{Vn}} = 1, 141, {{PP|40087|4713}}, {{PP|38112|5795}}, {{PP|37374|6611}}, {{PP|23436|18496}}, {{PP|17877|32292}}, {{PP|17850|32469}}, {{PP|10752|59656}}, {{PP|5931|90825}}, {{PP|271|262419}}, {{PP|102|361275}}, {{PP|77|481899}}, {{PP|75433|1354828}}, {{PP|87775|6328548}}, {{PP|89536|6679881}} and for no other {{Vn}} < {{Num|{{GP|Cullen prime 2|CuMaxn}}}} ({{OEIS|l|A005849}}).
  
The largest known Cullen prime is {{PP|89536|{{Num|6679881}} &times; 2<sup>{{Num|6679881}}</sup> + 1}} and the largest known generalized Cullen prime is {{PP|124515|{{Num|1806676}} &times; 41<sup>{{Num|1806676}}</sup> + 1}}.
+
The largest known Cullen prime is {{PP|89536|{{Kbn|+|6679881|6679881}}}} and the largest known generalized Cullen prime is {{PP|129893|{{Kbn|+|2805222|25|2805222}}}}.
  
 
==Current status==
 
==Current status==
*[http://www.primegrid.com/stats_cullen_llr.php Cullen search status] at [[PrimeGrid]]
+
*see [[Cullen prime 2|Cullen primes]]
 +
*see [[PrimeGrid Cullen Prime Search#Status|PrimeGrid Cullen Prime Search]]
  
 
==See also==
 
==See also==
Line 25: Line 26:
 
*[http://mathworld.wolfram.com/CullenNumber.html Mathworld]
 
*[http://mathworld.wolfram.com/CullenNumber.html Mathworld]
 
*[http://primes.utm.edu/glossary/xpage/Cullens.html The Prime Glossary]
 
*[http://primes.utm.edu/glossary/xpage/Cullens.html The Prime Glossary]
[[Category:Numbers]]
+
[[Category:Number]]

Latest revision as of 17:39, 31 August 2021