[33a]

Not unless you were very certainly sure it was true. The probability that you got it right and didn't mess up some detail is so vanishingly small that it might as well be 0.

If you go around shouting about yet another half-baked "solution", people will think you're a crank (and they might even be right). Exercise some restraint, check it and wait.

One thing about a positive P=NP proof is that it would necessarily be constructive, so you could try to actually implement it and maybe do some SAT solving competition. If you start stomping the competition, you would get noticed and be in a much stronger position to announce something like this.

[Someone]

"One thing about a positive P=NP proof is that it would necessarily be constructive"

I don't see why that would necessarily be true. For example, let's say that I show that, if P != NP, the set of all NP-complete problems can be split into N equivalence classes and then produce N+1 NP-complete problems that are pairwise in different equivalence classes.

Alternatively (and, I'm guessing, slightly more realistic), one might define a Turing-equivalent machine and show that, if there is any room between P and NP, for that machine, any program that solves a NP-complete problem can be reduced to run for one less time step.

Can you explain?