Let's call a prime number a $\textit{reversible prime}$ if the number formed by reversing its digits is also prime. What is the smallest reversible prime greater than 17?
I want to find a prime number whose reverse is also prime, and I want to start from the smallest possible candidates and work my way up. The next prime after 17 is 19, but reversing its digits gives 91, which is not prime (it is divisible by 7 and 13). The next prime after 19 is 23, but reversing its digits gives 32, which is not prime (it is divisible by 2 and 16). The next prime after 23 is 29, but reversing its digits gives 92, which is not prime (it is divisible by 2 and 46). The next prime after 29 is 31, but reversing its digits gives 13, which is prime. Therefore, the smallest reversible prime greater than 17 is 31.

