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## 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
*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 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

- MultiSieve to sieve a range of n
- LLR to test for primality (using the output from MultiSieve)

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 (*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: September 8, 2008