Proth 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 and 
is a natural number such that 
. The Proth number with parameters and is defined as the number:
.
A Proth number that is also a prime is termed a Proth prime.
Relation with other properties
Stronger properties
- Fermat number: The
Fermat number is the Proth number with 
and 
.
- Cullen number
- Mersenne number is a number of the form
.
- Sierpinski number is a number of the form
with 
