Definition:Cullen Prime

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Definition

A Cullen prime is a Cullen number:

$n \times 2^n + 1$

which is also prime.


Sequence

The sequence $\left\langle{n}\right\rangle$ for which $n \times 2^n + 1$ is a prime number begins:

$1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, \ldots$

This sequence is A005849 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Also defined as

Some sources refer to primes of the form $n \times 2^n - 1$ as also being Cullen primes.

However, it is now conventional to refer to numbers of the form $n \times 2^n - 1$ as Woodall primes, for Herbert J. Woodall.


Also known as

Some sources refer to Cullen primes as Cunningham primes, for Allan Joseph Champneys Cunningham, so as to ensure their distinction from Woodall primes.


Also see


Source of Name

This entry was named for James Cullen.


Sources