In other words, does the flat modify C[N] or does it modify the next C up, i.e., C[N+1]?
Melodic intervals are always measured from the lower note to the higher note, no matter which note comes first.
So yes, if the intervals between Cb and C is just a semitone apart, it’s an augmented prime.
- Cb to Cb: perfect prime
- Cb to C: one semitone bigger —> aug.
If the interval between Cb and C is one semitone greater than an octave, then it’s an augmented octave. :)