> it could be that P=NP, it could be that an algorithm exists to factor numbers to primes Nits but 1) even if P=NP, it is possible that the problems we've chos

> it could be that P=NP, it could be that an algorithm exists to factor numbers to primes Nits but 1) even if P=NP, it is possible that the problems we've chosen have a lower bound on their polynomial-time algorithms that still leaves them secure for the indefinite future (O(n^Graham's Number) is polynomial). Of course, we also don't have any proof of that so your general point stands. Related, 2) an algorithm certainly exists to find prime factors - quite a few actually! - but none that we know of in polynomial time without quantum computing.