An $\textit{emirp}$ is an integer that, when its digits are written in reverse order, is a prime number. For example, 73 is an emirp because 37 is prime. What is the smallest two-digit prime number that is NOT an emirp?
The smallest two-digit prime number is 11, but 11 reversed is also 11, which is prime, so 11 is an emirp. The next smallest two-digit prime number is 13, but 13 reversed is 31, which is also prime, so 13 is an emirp. The next smallest two-digit prime number is 17, but 17 reversed is 71, which is also prime, so 17 is an emirp. The next smallest two-digit prime number is 19, but 19 reversed is 91, which is not prime, since it is divisible by 7. Therefore, 19 is the smallest two-digit prime number that is not an emirp. 