Prime numbers are a fundamental part in the GMAT, so having questions such as these are a real blessing. Thanks emmak (you've earned a Kudos from me).
I'll kick this off by stating which concepts are going to be useful in solving this problem :
1/ Addition laws : ODD + EVEN = ODD, ODD + ODD = EVEN
2/ All prime numbers except 2 are ODD !!!
3/ Prime number list up until 31 (Yeah, it's harsh, but you need to know your prime numbers, otherwise, you'll be missing out on a lot of shortcuts)
Now, let's consider the answer choices.
You'll notice that all the answer choices except D are
odd. So there's got to be a 2 in the mix (if the question stem is correct) so :
A/ 19 = 2 + 17 (17 is prime, so cross off A) ;
B/ 25 = 2 + 23 (23 is prime, so cross off B) ;
C/ 33 = 2 + 31 (31 is prime, so cross off C) ;
D/ 46 = 23 + 23 (23 is prime, so cross off D);
This leaves us with answer choice E. And incidentally 51 IS a prime number.
An alternative to this method is to use the list of prime numbers up to 31 and make combinations. Depending on how comfortable you are with numbers, this can be a time-saver or a time-consuming method. So use at your own risk.
Hope that helped