Cullen number

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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


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.

Other related properties