2002 AMC 10B Problem 15

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

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

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