For how many two-digit primes is the sum of the digits equal to 8?
Hm...Thats a pretty good way! GJ!
To find out how many two-digit primes have a sum of digits equal to 8, we can go through each two-digit prime number and check if the sum of its digits is 8.
Step 1: Start with the smallest two-digit prime number, which is 11.
Step 2: Check if the sum of the digits of 11 (1 + 1) is equal to 8. It's not, so move on.
Step 3: Move to the next prime number, which is 13.
Step 4: Check if the sum of the digits of 13 (1 + 3) is equal to 8. It's not, so move on.
Step 5: Continue this process for each prime number less than 100, checking if the sum of the digits is equal to 8.
After going through all the two-digit prime numbers, we find that the numbers 17 and 71 have a sum of digits equal to 8.
Therefore, there are two two-digit prime numbers that have a sum of digits equal to 8.
To solve this problem, we need to find the total number of two-digit prime numbers whose digits add up to 8.
Let's break down the possible combinations of two-digit numbers whose digits add up to 8:
1. If the tens digit is 1, the ones digit can be any of the numbers (1, 2, 3, 4, or 5). However, 15 is not a prime number, so we cannot consider it.
2. If the tens digit is 2, the ones digit can be any of the numbers (6 or 2). But again, 26 is not a prime number, so we cannot consider it.
3. If the tens digit is 3, the ones digit can be any of the numbers (5 or 3). This gives us two possible numbers, which are 35 and 53.
4. If the tens digit is 4, the ones digit can be any of the numbers (4 or 0). But neither 40 nor 04 (which is just 4) is considered as a two-digit number.
5. If the tens digit is 5, the ones digit can only be 3. But 53 is already counted in point 3.
So, we have a total of two numbers (35 and 53), whose digits add up to 8, and both are prime numbers.
Therefore, there are two two-digit prime numbers whose digits add up to 8.
1 + 7 = 8 so 17 or 71
3 + 5 = 8 so ...... etc