17. (3 points) Given that $a$, $b$, and $c$ are three distinct prime numbers, if $a + b \times c = 37$, then the maximum value of $a + b - c$ is
【Solution】Solution: To maximize the value of $a+b-c$, we need to minimize the value of $c$. The smallest prime number is 2, so $c=2$; then we can get: $a=37-b \times c=37-2b$,

To maximize $a$, we need to minimize $b$, the smallest value for $b$ is 3, so the maximum value for $a$ is: $a=37-2 \times 3=31$, therefore, the maximum value of $a+b-c$ is: $a+b-c=31+3-2=32$; Answer: The maximum value of $a+b-c$ is 32. Therefore, the answer is: 32.