2009 AMC 12B Problem 19

For each positive integer n, let f(n) = n^4 - 360n^2 + 400. What is the sum of all values of f(n) that are prime numbers?

\textbf{(A)}\ 794\qquad \textbf{(B)}\ 796\qquad \textbf{(C)}\ 798\qquad \textbf{(D)}\ 800\qquad \textbf{(E)}\ 802

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.