Cullen Primes: Definition and Status

News Flash!

On August 23, 2005, Mark Rodenkirch found the largest known Cullen prime, 1354828*2^1354828+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 and for no other n < 5,000,000; Chris Caldwell maintains the top 20 Cullen Page.

A table of ranges of exponents that have already been tested or are reserved/available for current testing for Cullen primes is available.

A list of contributors to the Cullen project is here.

To search for Cullen primes, the recommended software is

To participate in a distributed search for Cullen primes, go here

To reserve a free range of n for one of the numbers above, check the most recent reserved values of n also and then click on the link on that page to reserve your range.

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 (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: September 8, 2008