AHSME 1983 Problem 3

Three primes $p,q$, and $r$ satisfy $p+q = r$ and $1 < p < q$. Then $p$ equals $\textbf{(A)}\ 2 \textbf{(B)}\ 3 \textbf{(C)}\ 7 \textbf{(D)}\ 13 \textbf{(E)}\ 17$