\begin{definition}[Definition:Proth Number]
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'''.
\end{definition}