2002 AMC 12B Problem 11

The positive integers A, B, A-B, and A+B are all prime numbers. The sum of these four primes is

\mathrm{(A)}\ \mathrm{even} \qquad\mathrm{(B)}\ \mathrm{divisible\ by\ }3 \qquad\mathrm{(C)}\ \mathrm{divisible\ by\ }5 \qquad\mathrm{(D)}\ \mathrm{divisible\ by\ }7 \qquad\mathrm{(E)}\ \mathrm{prime}

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