17. In a math test, there are 20 questions. Each correct answer earns 5 points, no answer earns 0 points, and each wrong answer deducts 2 points. If Xiaoli's score in this test is a prime number, then the maximum number of questions Xiaoli answered correctly is $\qquad$.
17.17.

Let Xiaoli answer $a$ questions correctly and $b$ questions incorrectly, with the score being $5a-2b<100$.
Since the score is a prime number, we have $5a-2b=97, 91, 89, 83, \cdots$. Only when $a=17, b=1$, $5a-2b=83$ is the largest prime number.
Therefore, Xiaoli answered at most 17 questions correctly this time.