A question about Goldbach's conjecture.

[Guest]

"Goldbach's conjecture states that every even number ≤ to 4 is the sum of two primes."

In my spare time, I proved that:

“If for every k ≥ 8 there exist primes p and q such that p < k < q < 2k and q - p = 2k, then k is the sum of two primes.”

In other words, “If a number is the difference of two primes, then it is the sum of two primes.”

Would this result be relevant, or is it a waste of time? Has anyone already proven this? In other words, would this be a sufficient result to prove the Strong Goldbach Conjecture.