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{{Last update|2019-02-27}}
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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 />
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a '''generalized Cullen number''' base ''b'' is a number of the form ''n'' &times; ''b''<sup>''n''</sup> + 1. '''(perhaps own page?)'''
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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}}).
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{{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}}.
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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]]
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*see [[Cullen prime 2|Cullen primes]]
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*see [[PrimeGrid Cullen Prime Search#Status|PrimeGrid Cullen Prime Search]]
  
 
==See also==
 
==See also==

Latest revision as of 17:39, 31 August 2021