[jMyles]

> "Broken" generally isn't a binary event in cryptography.

If there were, for example, a way to glean a private key without factoring the modulus, I think we'd all agree that this amounts to "breaking" the system insofar as that it changes the applicability of the hardness assumption.

On the other hand, simply achieving a faster way to factor the modulus is, at best, part of a continuum as you say.