AMC 12 2002b Problem 11

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

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