I was recently attempting to solve one of the more known, already proved, problems in mathematics when I stumbled across an observation I thought might be worth digging into further.
Unfortunately I have only been able to verify my observation up to a small few numbers but I am convinced that it holds true for all numbers? How or why, if I knew the answer I would be asking you guys how to go about submitting a proof :).
Anyway my question is, How do I submit my conjecture for a review, knowing fully well that it's just a conjecture and if it really does have some value a person reviewing it might claim it?
I do expect a certain degree of honesty from the committee members but in case I do not want to take any such risks, what is the best way to have my conjecture reviewed by knowledgeable people in the field without risking losing the "ownership" to the conjecture?
It honestly depends on who you talk to and how interesting and possibly tractable your conjecture is perceived to be. Usually a paper with only a conjecture in it will be rejected unless it's extremely well written and successfully explains how monumentally interesting it is. Every mathematician already has problems they are working on, and it's hard to convince someone to drop everything and work on something else unless it's extremely compelling.
In terms of ownership, that's always iffy and there are no guarantees about who will be remembered in a hundred years for thinking of what. It's extremely common for people to get it wrong. If it's marketable, though, you can try to get a patent. Plagiarism is unfortunately not illegal, it is merely reprehensible.
That said, there's no harm in telling people your conjecture if it's pure math. There are a couple of reasons for this:
Pure math very rarely wins you fame and fortune. It might get you some fame, but only in a very small community, and it can get you some grant money, but it's not worth killing for.
It's been observed that math is, at least compared to many other fields, generally honorable. Stealing other people's ideas is greatly frowned upon. If two people are working on the same thing and they find out about each other, and they decide not to collaborate, it's common for one of them to stop working on it so they don't tread on the other's territory.