Quickly, I have found a way to characterize the flip side of the way integer factorization all boils down to the Ascent:
The essential difficulty is the lumpiness of the whole Ceiling Root function: ceil(sqrt(m)). Even for prime numbers, it is not (yet) a smooth or closed-form derivation very much more easily managed than the distribution of prime numbers themselves.
So I’m barking up the right tree, arguably, but damn, is that tree tall!
Still, upward we must go, inasmuch as our climbing ability makes it possible.