AMC 12 2002a Problem 12

Both roots of the quadratic equation $x^2 - 63x + k = 0$ are prime numbers. The number of possible values of $k$ is

$\text{(A)}\ 0 \text{(B)}\ 1 \text{(C)}\ 2 \text{(D)}\ 4 \text{(E) more than 4}$