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Difference between revisions of "Woodall prime"
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A '''Woodall prime''' is a [[Woodall number]] ({{Kbn|n|2|n}}), which is [[prime]]. | A '''Woodall prime''' is a [[Woodall number]] ({{Kbn|n|2|n}}), which is [[prime]]. | ||
| − | A ''' | + | A '''Generalized Woodall prime''' could be defined as a Woodall prime with a general base {{Vb}} > 2, so of the form {{Kbn|n|b|n}}. |
The restriction of {{Vn}}+2 > {{Vb}} should then be claimed, otherwise every prime could be called a "Generalized Woodall prime". | The restriction of {{Vn}}+2 > {{Vb}} should then be claimed, otherwise every prime could be called a "Generalized Woodall prime". | ||
| + | A '''Near Generalized Woodall prime''' is defined as '''[[:Category:Woodall prime M|{{Kbn|(n-1)|b|n}}]]''' or '''[[:Category:Woodall prime P|{{Kbn|(n+1)|b|n}}]]'''. | ||
==Note== | ==Note== | ||
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 Woodall primes". | 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 Woodall primes". | ||
| Line 15: | Line 16: | ||
==External links== | ==External links== | ||
*[[Wikipedia:Woodall_number|Woodall number]] | *[[Wikipedia:Woodall_number|Woodall number]] | ||
| − | *[https:// | + | *[https://t5k.org/glossary/page.php?sort=WoodallNumber Woodall number] |
| − | *[https:// | + | *[https://t5k.org/top20/page.php?id=45 Top 20 Generalized Woodall primes] |
| − | *[ | + | *[https://harvey563.tripod.com/GWNews.txt Generalized Woodall status reports] by [[Steven Harvey]], 2019-04-13 |
| − | *[https://www.mersenneforum.org/showthread.php?t=19713 | + | *[https://harvey563.tripod.com/gwranges.txt Generalized Woodall ranges completed] by [[Steven Harvey]], 2019-03-29 |
| + | *[https://harvey563.tripod.com/GeneralizedWoodallPrimes.txt Generalized Woodall primes] by [[Steven Harvey]], 2019-04-15 | ||
| + | *[https://harvey563.tripod.com/NearGeneralizedWoodall.txt Near Generalized Woodall primes] by [[Steven Harvey]], 2017-08-11 | ||
| + | *[https://www.mersenneforum.org/showthread.php?t=28553 Current reservation/status: 2023-04-01 to (ongoing)] at [[MersenneForum]] | ||
| + | *[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]] | ||
[[Category:Woodall prime| ]] | [[Category:Woodall prime| ]] | ||
Latest revision as of 17:13, 28 October 2024
Contents
Definitions
A Woodall prime is a Woodall number (n•2n-1), which is prime.
A Generalized Woodall prime could be defined as a Woodall 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 Woodall prime".
A Near Generalized Woodall prime is defined as (n-1)•bn-1 or (n+1)•bn-1.
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 Woodall primes".
See also
- original Woodall primes list
- Table with all available bases
External links
- Woodall number
- Woodall number
- Top 20 Generalized Woodall primes
- Generalized Woodall status reports by Steven Harvey, 2019-04-13
- Generalized Woodall ranges completed by Steven Harvey, 2019-03-29
- Generalized Woodall primes by Steven Harvey, 2019-04-15
- Near Generalized Woodall primes by Steven Harvey, 2017-08-11
- 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
