The strengthened Golbach conjecture (not an official name, there doesn't appear to be a commonly used name for it) is the conjecture that every even number greater than 6 can be written as the sum of two distinct primes. The only difference between this and the usual Goldbach conjecture is that it also implies that there is a second Golbach partition for any number that can be written as 2p for p prime (except 4 and 6).

This would imply /JosephNoonan/if-5-the-only-odd-untouchable-numbe

See also:

%Is Golbach's Conjecture correct?

/JosephNoonan/is-the-preprint-proof-of-goldbachs