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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 | + | 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 "Cullen primes". |
==See also== | ==See also== | ||
| − | * | + | *[[Cullen prime 2|Cullen primes base 2]] list |
| − | *[[ | + | *[[Cullen prime table|Table]] with all available bases |
==External links== | ==External links== | ||
*[[Wikipedia:Cullen_number|Cullen number]] | *[[Wikipedia:Cullen_number|Cullen number]] | ||
| − | *[https:// | + | *[https://t5k.org/top20/page.php?sort=Cullen Cullen number] |
| − | *[https:// | + | *[https://t5k.org/top20/page.php?id=42 Top 20 Generalized Cullen primes] |
| − | *[http://www.loeh.name/guenter/gc/status.html List for | + | *[http://www.loeh.name/guenter/gc/status.html List for 3 ≤ b ≤ 100] by [[Günter Löh]], 2019-11-23 |
| − | *[http://harvey563.tripod.com/GClist.txt List for 101 ≤ b ≤ 10000] by | + | *[http://harvey563.tripod.com/GClist.txt List for 101 ≤ b ≤ 10000] by [[Steven Harvey]] |
| − | *[https://www.mersenneforum.org/showthread.php?t=19713 | + | *[http://prothsearch.com/GC-Discoverers.html Discoverers for 3 ≤ b ≤ 200] by [[Wilfrid Keller]], occasionally updated |
| − | *[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by Daniel Hermle (WaybackMachine) | + | *[https://www.mersenneforum.org/showthread.php?t=28553 Current reservation/status: 2023-04-01 to (ongoing)] at [[MersenneForum]] |
| − | [[Category: | + | *[https://www.mersenneforum.org/showthread.php?t=28531 Generalized Cullens/Woodalls: 2023-03-13 to 2023-04-03] at [[MersenneForum]] |
| + | *[https://www.mersenneforum.org/showthread.php?t=24778 Some new Generalized Cullen and Woodall primes: 2019-09-02 to 2019-11-27] at [[MersenneForum]] | ||
| + | *[https://www.mersenneforum.org/showthread.php?t=19935 Generalized Cullen/Woodall Sieving Software: 2014-11-05 to 2014-12-29] at [[MersenneForum]] | ||
| + | *[https://www.mersenneforum.org/showthread.php?t=19713 Generalized Cullen and Woodall Searches: 2014-09-21 to 2022-02-12] at [[MersenneForum]] | ||
| + | *[http://web.archive.org/web/20070626212719/http://www.primzahlenarchiv.de/index.html Old pages] by [[Daniel Hermle]] (WaybackMachine) | ||
| + | [[Category:Cullen prime| ]] | ||
Latest revision as of 22:58, 22 November 2024
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 "Cullen primes".
See also
- Cullen primes base 2 list
- Table with all available bases
External links
- Cullen number
- Cullen number
- Top 20 Generalized Cullen primes
- List for 3 ≤ b ≤ 100 by Günter Löh, 2019-11-23
- List for 101 ≤ b ≤ 10000 by Steven Harvey
- Discoverers for 3 ≤ b ≤ 200 by Wilfrid Keller, occasionally updated
- Current reservation/status: 2023-04-01 to (ongoing) at MersenneForum
- Generalized Cullens/Woodalls: 2023-03-13 to 2023-04-03 at MersenneForum
- Some new Generalized Cullen and Woodall primes: 2019-09-02 to 2019-11-27 at MersenneForum
- Generalized Cullen/Woodall Sieving Software: 2014-11-05 to 2014-12-29 at MersenneForum
- Generalized Cullen and Woodall Searches: 2014-09-21 to 2022-02-12 at MersenneForum
- Old pages by Daniel Hermle (WaybackMachine)
