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Difference between revisions of "Cullen prime"
m (Karbon moved page Gen. Cullen prime to Gen Cullen prime without leaving a redirect: renamed) |
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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 | + | 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 | + | 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 | + | 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 "Gen Cullen primes". |
==See also== | ==See also== | ||
− | *original [[Gen | + | *original [[Gen Cullen prime 2|Cullen primes]] list |
− | *[[Gen | + | *[[Gen Cullen prime table|Table]] with all available bases |
==External links== | ==External links== | ||
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*[https://www.mersenneforum.org/showthread.php?t=19713 Thread] at [[MersenneForum]] | *[https://www.mersenneforum.org/showthread.php?t=19713 Thread] at [[MersenneForum]] | ||
*[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by Daniel Hermle (WaybackMachine) | *[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by Daniel Hermle (WaybackMachine) | ||
− | [[Category:Gen | + | [[Category:Gen Cullen prime| ]] |
Revision as of 10:26, 2 November 2020
Contents
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 n•bn+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 n•bn+1 are given with b ≥ 2, n ≥ 1 and listed as "Gen Cullen primes".
See also
- original Cullen primes list
- Table with all available bases
External links
- Cullen number
- Cullen number
- Top 20 Generalized Cullen primes
- List for 2 ≤ b ≤ 100 by Günther Löh, 2018-08-14
- List for 101 ≤ b ≤ 10000 by S.Harvey
- Thread at MersenneForum
- Old pages by Daniel Hermle (WaybackMachine)