goldbach conjecture proof

[praharmitra]

is there a proof for the goldbach's conjecture????

that the every number can be written as the sum of three primes....
or, every even integer can be written as the sum of two primes??

[Gokul43201]

Not yet.

[CRGreathouse]

I think Vinogradov proved that there is some (huge) n beyond which ternary Goldbach holds. I don't think we know even that in the binary case.

[Dodo]

Correct me if I'm wrong, but there is no need to refer to the sum-of-three-primes case, since a proof of the sum-of-two would immediately provide a sum of three primes for any integer >= 6. Just subtract 2 or 3, depending on whether your number is even or odd respectively, and then use the sum-of-two on the resulting even number. Right?

[LukeD]

Sure, but the ternary case doesn't immediately imply the binary one (as far as I know), so they're not equivalent, and the ternary case could be easier to prove.

[CRGreathouse]

Correct me if I'm wrong, but there is no need to refer to the sum-of-three-primes case, since a proof of the sum-of-two would immediately provide a sum of three primes for any integer >= 6. Just subtract 2 or 3, depending on whether your number is even or odd respectively, and then use the sum-of-two on the resulting even number. Right?

The binary implies the ternary, that's why they're both considered versions of the same problem. But the binary version is much harder.