# Proth number

From Number

## 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