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 Cn = n*2n+1.

Cn 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, although Daniel's website is no longer available.

Woodall numbers (Wn = n*2n-1) are related to Cullen numbers and are sometimes called Cullen numbers of the second kind. Check here for the Woodall prime search.

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

Last Modified: August 31, 2014