2007 Fermat Problem 13

In the diagram, each of the numbers 0, 1, 2, 3, 4, 5, 6, and 7 is to be used to label a vertex of the cube. The numbers 0, 2 and 3 are placed as shown. The sum of the numbers at the ends of each edge must be a prime number. (Note: 1 is not a prime number.) The value of M + N + P + Q must be

\textbf{(A)}\ 16\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 18\quad \textbf{(D)}\ 19\quad \textbf{(E)}\ 22

If there are no answer choices shown, enter a numerical answer.

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