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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 '''"Generalized Woodall prime"''' could be defined as a Woodall prime with a general base | + | 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 | + | The restriction of {{Vn}}+2 > {{Vb}} should then be claimed, otherwise every prime could be called a "Generalized Woodall 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 Woodall primes". |

==See also== | ==See also== | ||

− | *original [[ | + | *original [[Woodall prime 2|Woodall primes]] list |

− | *[[ | + | *[[Woodall prime table|Table]] with all available bases |

==External links== | ==External links== | ||

Line 19: | Line 19: | ||

*[http://harvey563.tripod.com/GeneralizedWoodallPrimes.txt Exhaustive list] by S.Harvey | *[http://harvey563.tripod.com/GeneralizedWoodallPrimes.txt Exhaustive list] 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: | + | [[Category:Woodall prime| ]] |

## Latest revision as of 16:40, 31 August 2021

## Contents

## Definitions

A **Woodall prime** is a Woodall number (`n`•2^{n}-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`•`b`^{n}-1.
The restriction of `n`+2 > `b` should then be claimed, otherwise every prime could be called a "Generalized Woodall prime".

## Note

For a complete list in this Wiki the primes of the forms `n`•`b`^{n}-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