# Proth 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

## 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.