For how many two-digit prime numbers is the sum of its digits 8?
I need to find two-digit prime numbers that have a digit sum of 8. I can start by listing some candidates that have a digit sum of 8, regardless of whether they are prime or not. The candidates are 17, 26, 35, 44, 53, 62, 71, and 80. I can eliminate some of them immediately, since they are divisible by 2, 4, or 5. I can check if they are prime by dividing them by some small primes, such as 3, 7, and 11. 17 is not divisible by any of these, so it is prime. 35 is divisible by 5 and 7, so it is not prime. 53 is not divisible by any of these, so it is prime. 71 is not divisible by any of these, so it is prime. Therefore, there are three two-digit prime numbers that have a digit sum of 8: 17, 53, and 71. 