2011 AMC 8 Problem 24

In how many ways can 10001 be written as the sum of two primes?

\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4

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