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# (Generalized) Cullen primes

## Contents

## Definitions

A **Cullen prime** is a Cullen number (`n`•2^{n}+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`•`b`^{n}+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`•`b`^{n}+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 2 ≤ b ≤ 100 by Günter Löh, 2019-11-23
- List for 101 ≤ b ≤ 10000 by Steven Harvey
- Current reservation/status: 2023-04-01 to 2023-05-07 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)