Problem:
The positive integers , and are all prime numbers. The sum of these four primes is
Answer Choices:
A. even
B. divisible by 3
C. divisible by 5
D. divisible by 7
E. prime
Solution:
The numbers and are both odd or both even. However, they are also both prime, so they must both be odd. Therefore, one of and is odd and the other even. Because is a prime between and must be the odd prime. Therefore, , the only even prime. So , and are consecutive odd primes and thus must be 3,5 , and 7 . The sum of the four primes , and 7 is the number 17 .
The problems on this page are the property of the MAA's American Mathematics Competitions