Nor would it necessarily work (quickly) if the order of magnitude for any constants were sufficiently large (after all, a runtime of 2 * N and a runtime of (2^5

Nor would it necessarily work (quickly) if the order of magnitude for any constants were sufficiently large (after all, a runtime of 2 * N and a runtime of (2^512) * N are both O(N)). If I remember correctly, in the semi-regular survey conducted with CS experts about this question, the most likely explanation that accompanied a response saying they believed that it may be the case that P=NP was “...but with very large constants”.