Cullen prime

A Cullen prime is a Cullen numberMathworldPlanetmath Cm that is also a prime numberMathworldPlanetmath. The first two Cullen primes are 3 and 393050634124102232869567034555427371542904833, corresponding to m=1 and 141 respectively; other m to give Cullen primes are 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, etc. listed in A005849 of Sloane’s OEIS (those primes being too large to write here). None of these indexes are prime, and it is a matter of conjecture whether there exists a Cullen prime of the form p2p+1 with p also prime. It is not even known whether there are infinitely many Cullen primes (a possibility despite their rarity).

Title Cullen prime
Canonical name CullenPrime
Date of creation 2013-03-22 17:21:37
Last modified on 2013-03-22 17:21:37
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51