AMC 12 2002b Problem 3

For how many positive integers $n$ is $n^2 - 3n + 2$ a prime number?

$\mathrm{(A)}\ \text{none} \mathrm{(B)}\ \text{one} \mathrm{(C)}\ \text{two} \mathrm{(D)}\ \text{more\ than\ two,\ but\ finitely\ many} \mathrm{(E)}\ \text{infinitely\ many}$