(Generalized) Cullen primes

Definitions

A Cullen prime is a Cullen number (n•2ⁿ+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•bⁿ+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•bⁿ+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 3 ≤ b ≤ 100 by Günter Löh, 2019-11-23
• List for 101 ≤ b ≤ 10000 by Steven Harvey
• Discoverers for 3 ≤ b ≤ 200 by Wilfrid Keller, occasionally updated
• 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
• Old pages by Daniel Hermle (WaybackMachine)