Prime in a binary string

You are given a binary string $S$ of length $N$. Your task is to check if there exists a [substring](https://en.wikipedia.org/wiki/Substring) of $S$ which is the binary representation of a [prime number](https://en.wikipedia.org/wiki/Prime_number). Formally, check if there exist integers $L$ and $R$ such that $1 \leq L \leq R \leq N$, and the substring $S_L S_{L+1} S_{L+2} \ldots S_R$, when treat