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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". | ||
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*[https://primes.utm.edu/glossary/page.php?sort=WoodallNumber Woodall number] | *[https://primes.utm.edu/glossary/page.php?sort=WoodallNumber Woodall number] | ||
*[https://primes.utm.edu/top20/page.php?id=45 Top 20 Generalized Woodall primes] | *[https://primes.utm.edu/top20/page.php?id=45 Top 20 Generalized Woodall primes] | ||
− | *[ | + | *[https://harvey563.tripod.com/GeneralizedWoodallPrimes.txt Generalized Woodall primes] by S.Harvey |
+ | *[https://harvey563.tripod.com/NearGeneralizedWoodall.txt Near Generalized Woodall primes] by S.Harvey | ||
*[https://www.mersenneforum.org/showthread.php?t=19713 Thread] at [[MersenneForum]] | *[https://www.mersenneforum.org/showthread.php?t=19713 Thread] at [[MersenneForum]] | ||
[[Category:Woodall prime| ]] | [[Category:Woodall prime| ]] |
Revision as of 09:53, 13 March 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