# Definition:Cullen Prime

## Definition

A Cullen prime is a Cullen number:

$n \times 2^n + 1$

which is also prime.

### Sequence

The sequence $\sequence n$ for which $n \times 2^n + 1$ is a prime number begins:

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

## 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.

## Source of Name

This entry was named for James Cullen.