This was originally going to be a comment, but I realized it's more of an answer.
Perhaps the first question you might want to ask should be: Is this equivalent to Goldbach's conjecture? If you explain why you think it is, that should be sufficient context. As a side note, if I'm reading the link correctly, I'm pretty sure it's not equivalent. Note that the poly at the link doesn't necessarily produce all primes, and only its positive values are prime. Its negative values are not necessarily prime. (Also, it has (lots of) negative values, which would also be a problem, no?)
Lastly, the question you've asked about here would be on topic, given adequate context, but I'm not really sure that would make it either a good question or cause you to get an answer that you'd like. What exactly would you be looking for in a solution to your question? A proof of the Goldbach conjecture? Forgive me if I think that seems unlikely to occur.
Also to be clear, I don't think you've provided adequate context here. Your question as written here is:
This is equivalent to the Goldbach conjecture. Can someone show me how to prove it?
Context you might want to add is
- A proof of equivalence to the Goldbach conjecture, or
- Alternatively a reference that actually shows that it's equivalent.
- If you want to prove it by induction, at least prove the base case, and show us where you're getting stuck with the inductive step.
The moral of the story here is that when asking a question, you should generally explain two things
- Why you want to solve it, and
- where you're getting stuck.
I see neither of those at present.