We have no evidence that factoring is NP-hard, and some evidence that it probably isn’t: the best known classical algorithms for factoring are much faster than

We have no evidence that factoring is NP-hard, and some evidence that it probably isn’t: the best known classical algorithms for factoring are much faster than those for NP-complete problems. We have no idea whether NP = BQP, or indeed whether either is contained in the other.