We have : \(P+Q>P-Q\ge2\), so P + Q is odd and P > Q

Then, one of them is odd and the another is even. Because 2 is the only even prime and is the smallest prime, Q = 2

If P - 2 = 3k + 1, then P + 2 = 3k + 3 is a composite

If P - 2 = 3k + 2, then P + 2 = 3k + 6 is a composite

So, P - 2 = 3k <=> k = 1 <=> P - 2 = 3 <=> P = 5

The answer is : P + Q + P + Q + P - Q = 3P + Q = 17

Nguyễn Đặng Hoàng Phúc, p - 2 is prime and p - 2 = 3k, so k = 1

Phan Thanh Tinh Wrong:P-2=3k+1 then P=3k+3 

Why P-2=3k\(\Leftrightarrow\)k=1