# Category:Proth Numbers

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This category contains results about Proth Numbers.

Definitions specific to this category can be found in Definitions/Proth Numbers.

A **Proth number** is a natural number of the form:

- $N = k \times 2^n + 1$

where:

- $k$ is an odd integer
- $n$ is a positive integer
- $2^n > k$

The condition is included, otherwise every odd integer greater than $1$ would be a **Proth number**.