Find the smallest two-digit prime number such that reversing the digits of the number produces a composite number.
I know that a prime number is a positive integer that has exactly two factors: 1 and itself. I also know that a composite number is a positive integer that has more than two factors. To find the smallest two-digit prime number, I can start from the lowest possible value and work my way up until I find one that satisfies the condition. The lowest possible two-digit number is 10, but that is not prime because it is divisible by 2 and 5. The next one is 11, which is prime, but reversing the digits gives 11, which is also prime. The next one is 12, which is not prime because it is divisible by 2, 3, 4, and 6. The next one is 13, which is prime, but reversing the digits gives 31, which is also prime. The next one is 14, which is not prime because it is divisible by 2 and 7. The next one is 15, which is not prime because it is divisible by 3 and 5. The next one is 16, which is not prime because it is divisible by 2, 4, and 8. The next one is 17, which is prime, but reversing the digits gives 71, which is also prime. The next one is 18, which is not prime because it is divisible by 2, 3, 6, and 9. The next one is 19, which is prime, and reversing the digits gives 91, which is composite because it is divisible by 7 and 13. Therefore, the smallest two-digit prime number that satisfies the condition is 19. 