  Let $n$ be a positive integer greater than $2$. We define \textit{the Proth
numerical semigroup}, $P_{k}(n)$, generated by $\{k 2^{n+i}+1 \,\mid\, i \in
\mathbb{N}\}$, where $k$ is an odd positive number and $k < 2^{n}$. In this
paper, we introduce the Frobenius problem for the Proth numerical semigroup
$P_{k}(n)$ and give formulas for the embedding dimension of $P_{k}(n)$. We
solve the Frobenius problem for $P_{k}(n)$ by giving a closed formula for the
Frobenius number. Moreover, we show that $P_{k}(n)$ has an interesting property
such as being Wilf.
