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Difference between revisions of "Cullen prime"

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A '''Cullen prime''' is a [[Cullen number]] ({{Kbn|+|n|2|n}}), which is [[prime]].
 
A '''Cullen prime''' is a [[Cullen number]] ({{Kbn|+|n|2|n}}), which is [[prime]].
  
A '''"Generalized Cullen prime"''' could be defined as a Cullen prime with a general base ''b'' > 2, so of the form {{Kbn|+|n|b|n}}.
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A '''"Generalized Cullen prime"''' could be defined as a Cullen prime with a general base {{Vb}} > 2, so of the form {{Kbn|+|n|b|n}}.
The restriction of ''n''+2 > ''b'' should then be claimed, otherwise every prime could be called a "Generalized Cullen prime".
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The restriction of {{Vn}}+2 > {{Vb}} should then be claimed, otherwise every prime could be called a "Generalized Cullen prime".
  
 
==Note==
 
==Note==
For a complete list in this Wiki the primes of the forms {{Kbn|+|n|b|n}} are given with ''b'' ≥ 2, ''n'' ≥ 1 and listed as "Gen. Cullen primes".
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For a complete list in this Wiki the primes of the forms {{Kbn|+|n|b|n}} are given with {{Vb}} ≥ 2, {{Vn}} ≥ 1 and listed as "Cullen primes".
  
 
==See also==
 
==See also==
*original [[Gen. Cullen prime 2|Cullen primes]] list
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*[[Cullen prime 2|Cullen primes base 2]] list
*[[Gen. Cullen prime table|Table]] with all available bases
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*[[Cullen prime table|Table]] with all available bases
  
 
==External links==
 
==External links==
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*[https://primes.utm.edu/top20/page.php?sort=Cullen Cullen number]
 
*[https://primes.utm.edu/top20/page.php?sort=Cullen Cullen number]
 
*[https://primes.utm.edu/top20/page.php?id=42 Top 20 Generalized Cullen primes]
 
*[https://primes.utm.edu/top20/page.php?id=42 Top 20 Generalized Cullen primes]
*[http://www.loeh.name/guenter/gc/status.html List for 2 ≤ b ≤ 100] by Günther Löh, 2018-08-14
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*[http://www.loeh.name/guenter/gc/status.html List for 2 ≤ b ≤ 100] by [[Günter Löh]], 2019-11-23
*[http://harvey563.tripod.com/GClist.txt List for 101 ≤ b ≤ 10000] by S.Harvey
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*[http://harvey563.tripod.com/GClist.txt List for 101 ≤ b ≤ 10000] by [[Steven Harvey]]
*[https://www.mersenneforum.org/showthread.php?t=19713 Thread] at [[MersenneForum]]
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*[https://www.mersenneforum.org/showthread.php?t=28553 Current reservation/status: 2023-04-01 to 2023-05-07] at [[MersenneForum]]
*[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by Daniel Hermle (WaybackMachine)
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*[https://www.mersenneforum.org/showthread.php?t=28531 Generalized Cullens/Woodalls: 2023-03-13 to 2023-04-03] at [[MersenneForum]]
[[Category:Gen._Cullen_prime| ]]
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*[https://www.mersenneforum.org/showthread.php?t=24778 Some new Generalized Cullen and Woodall primes: 2019-09-02 to 2019-11-27] at [[MersenneForum]]
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*[https://www.mersenneforum.org/showthread.php?t=19935 Generalized Cullen/Woodall Sieving Software: 2014-11-05 to 2014-12-29] at [[MersenneForum]]
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*[https://www.mersenneforum.org/showthread.php?t=19713 Generalized Cullen and Woodall Searches: 2014-09-21 to 2022-02-12] at [[MersenneForum]]
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*[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by [[Daniel Hermle]] (WaybackMachine)
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[[Category:Cullen prime| ]]

Revision as of 17:22, 7 May 2023

Definitions

A Cullen prime is a Cullen number (n•2n+1), which is prime.

A "Generalized Cullen prime" could be defined as a Cullen prime with a general base b > 2, so of the form nbn+1.

The restriction of n+2 > b should then be claimed, otherwise every prime could be called a "Generalized Cullen prime".

Note

For a complete list in this Wiki the primes of the forms nbn+1 are given with b ≥ 2, n ≥ 1 and listed as "Cullen primes".

See also

External links