After a few restless nights, thinking about prime numbers, it finally dawned on me. . .
Heuristically, every natural number, N, greater than 3, contains at least one 2 number partition a:b, which always fulfils the following conditions:
1. a is a prime number less than N
2. b is an odd number (not necessarily prime) OR an even number
3. a plus 2b equals another prime number (p) which is greater than N
4. a plus p equals 2N
This would explain why the GC is correct, and I would have thought that the maths of partitions should be able to prove the conditions, 1 - 4. Alas, it seems I have just been re-arranging the deck chairs on the Titanic, so for me it's back to the drawing board, unless someone out there knows better . . .