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# Cullen number

A **Cullen number** `C _{n}` is a number of the form

`n`•2

^{n}+1,

a **generalized Cullen number** base `b` is a number of the form `n`•`b`^{n}+1. **(perhaps own page?)**

## Cullen primes

`C _{n}` is prime for

`n`= 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 and for no other

`n`< 21,000,000 (sequence A005849 in OEIS).

The largest known Cullen prime is 6679881•2^{6679881}+1 and the largest known generalized Cullen prime is 2805222•25^{2805222}+1.

## Current status

## See also

## External links

- Top 20 Cullen Primes
- Top 20 Generalized Cullen Primes
- The Chronology of Prime Number Records
- Web archive "prothsearch.net"
- Generalized Cullen Search, Günter Löh (3 ≤ base ≤ 100), dated Sept. 2017
- Web archive "primzahlenarchiv.de", Daniel Hermle (101 ≤ base ≤ 200), dated 2007
- Generalized Cullen, Steven Harvey (101 ≤ base ≤ 10000), dated 2017
- Cullen number
- Mathworld
- The Prime Glossary