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Find the three digit prime number whose sum of the digit is 11 and each digit representing a prime number. Justify your answer.
Since the sum of the 3-digits is II and each digit represents a prime number.
So the 3-digits may be 2, 2, 7 or 3, 3, 5 because 2+2+7=11 and 3+3+5=11
Now using the digit 2, 2, 7 we have the prime number 227. Because other two numbers i.e. 722 and 272 are by 2 and thus are not prime.
Again, using the digit 3, 3, 5 we have the number 353 which is a prime number. But 533 which is divisible by 13 and thus 533 is not prime and 335 is divisible by 5 and thus 335 is not prime.
So, the three-digit prime number whose sum of the digits is 11 and each digit representing a prime number is 227 & 353. (Answer)
