[Math] The Number of Two-digit Primes Which the Sum of their Digits is 6

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Problem: Find the number of two-digit primes which the sum of their digits is six.

We had this problem in a mathematic examination. The problem can be solved by testing all two-digit primes, but I wish a more mathematical solution.

Best Answer

We know that a number whose sum of digits is divisible by 3 is divisible by 3. Since we argue about 2 digit numbers, every such number whose digits add up to 6 is divisible by 3 and hence not a prime.

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