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 .
