Problem:
Let be the least prime number that can be written as the sum of 5 distinct prime numbers. What is the sum of the digits of ?
Answer Choices:
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Solution:
The prime 2 cannot be among the 5 distinct primes chosen because, if it were, then the sum would be even. The first 5 odd primes are , and 13 , and their sum is 39 , which is not prime. The next smallest sum of 5 distinct odd primes is , which is prime. The requested digit sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions