I just noticed a limitation.
All prime numbers, except 2 are odd. Furthermore, if you add two odd numbers, you get an even number, which are never prime numbers. This means that, to get an odd number, you need both an odd and even number. Since the only even prime number is 2, all the prime numbers that can be formed from the sum of two primes have a two in their sum.
Let n be a prime number. Because of all the reasons listed above, the only solution is to do 2+(n-2). Because n-2 must be a prime number, prime numbers that are the sum of two prime numbers have to have a prime number n and a prime number n-2. This means that they must be part of a double prime (the greater of the two). This makes this thread unnecessarily easy and almost completely useless. I rest my case.