I have a few questions on GWC, as the Wikipedia's page on it appears to be somewhat incomplete.
Which of the following two statements is considered as the actual GWC?
- Every odd number greater than 5 can be expressed as the sum of three primes
- Every odd number greater than 7 can be expressed as the sum of three odd primes
The first statement is easily implied from GSC, but the second statement doesn't appear to be so (at least not easily)... So unless I'm overlooking something here, these two statements seem far from being equivalent to each other.
Has it really been proved or only claimed proved by Harald Helfgott?