Charlotte is playing the hit new web number game, Primle. In this game, the objective is to guess a two-digit positive prime integer between $10$ and $99$, called the Primle. For each guess:

- A digit is highlighted blue if it is in the Primle but not in the correct place.
- A digit is highlighted orange if it is in the Primle and is in the correct place.
- A digit is left unhighlighted if it is not in the Primle.

If Charlotte guesses $13$ and $47$ and is left with the following game board, what is the Primle?

$$
\begin{array}{c} 
    \boxed{1} \quad \boxed{3} \\
    \boxed{4} \quad \fcolorbox{black}{blue}{\color{white}7}
\end{array}
$$

Let's think step by step and output the final answer within \boxed{}.
user