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# (Generalized) Woodall primes

## 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".

A **Near Generalized Woodall prime** is defined as ** (n-1)•b^{n}-1** or

**.**

`(n+1)`•`b`^{n}-1## 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

## 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