## Cullen Primes: Definition and Status

### News Flash!

**On August 1, 2009, Magnum Bergman (working with PrimeGrid)
found the largest known Cullen prime, 6679881*2^6679881+1**

### News Flash!

**On April 20, 2009, Dennis R. Gesker (working with PrimeGrid)
found the largest known Cullen prime, 6328548*2^6328548+1**

Cullen Primes are Cullen numbers that are prime and of the form
*C*_{n} = *n* · 2^{n} + 1 .

*C*_{n }is prime for *n* = 1, 141,
4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419,
361275, 481899, 1354828, 6328548 and for no other *n* __<__ 10,000,000; Chris Caldwell maintains the
top 20 Cullen Page.

A list of contributors to the Cullen project is here.

PrimeGrid is coordinating a
distributed search for Cullen primes using BOINC.

To search for Cullen Primes of other bases, check out Günter Löh's
Generalized Cullen Search for 3 ≤ b ≤ 100 and
Daniel Hermle's Generalized Cullen Search for 101 ≤ b ≤ 200.

Woodall numbers (*W*_{n} = *n* · 2^{n} − 1)
are related to Cullen numbers and are sometimes called Cullen numbers of the second kind. Check
here for the Woodall prime search.

Back to index Page

If you have any questions about the Cullen Search, you can e-mail
Mark Rodenkirch or
Ray Ballinger

URL: http://www.prothsearch.net/cullen.html

Last Modified: March 19, 2013