SOLUTION: The positive integers p,q. p-q and p+q are all prime numbers. The sum of all these numbers is

Question 851579: The positive integers p,q. p-q and p+q are all prime numbers. The sum of all these numbers is
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
p-q and p+q have the same parity; since they are both positive and both prime, p-q and p+q must both be odd. It follows that either p or q is 2. If p = 2, then q > 2, and p-q is negative. If q = 2, then p-2, p, p+2 must be prime, and the only prime p such that this works is p = 5. The sum of the numbers is 5 + 2 + 3 + 7 = 17.
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