【Answer】Solution: The prime numbers that are two-digit numbers are: $11,13,31,17,71,37,73,79,97$, a total of 9.
Answer: $\overline{\mathrm{ab}}$ has 9.
Therefore, the answer is: 9.
13. (6 points) Both two-digit numbers $\overline{a b}$ and $\overline{\mathrm{ba}}$ are prime numbers, then $\overline{a b}$ has $\qquad$.

保留源文本的换行和格式，直接输出翻译结果如下：

13. (6 points) Both two-digit numbers $\overline{a b}$ and $\overline{\mathrm{ba}}$ are prime numbers, then $\overline{a b}$ has $\qquad$.
