# Cullen number

From Number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.

View a complete list of properties of natural numbers

## Contents

## Definition

Suppose is a natural number. The **Cullen number** parametrized by , denoted , is defined as:

A Cullen number that is a prime is termed a Cullen prime.

## Relation with other properties

### Weaker properties

- Proth number: A Proth number is a number of the form , . Since for all , any Cullen number is a Proth number.
- Generalized Cullen number: A Cullen number of the form where . Note that the special case where gives Cullen numbers.

- Fermat number is a number of the form , and is also a special case of a Proth number.
- Sierpinski number is a number of the form , with .