I'm reading a paper regrading the basis orders. In that paper, I met with the following statement:
$$3(\mathbb{P}\cup\{0 \})=\mathbb{Z}_{\geq 2}$$,
Which, by definition, states that primes form basis of order $3$(Must admit that I still don't really know what it really means).
My question is, why the statement "every integer greater than $2$ can be represented as sum of three prime" equivalent to Goldbach's conjecture.