A3/A4 = The Prime Octave.

When talking a lot about tuning in a technical way, descriptive shortcuts are inevitable.  Referring to the A3/A4 octave as the “Prime” octave came about as one of those shortcuts.  Soon after that, the term ‘Sub-Prime’ was used to describe or identify the A2-A3 octave.

Both prime and subprime terms are used here to quickly denote the A3/A4 and the A2/A3 octaves.  Whether it’s an interval or a range is generally determined in how they are used in conversation.  The ‘prime’ octave is referred to as both an interval and as a ‘range’ of notes.
The ‘subprime’ octave can also refer to the interval A2/A3, but most of the time the subprime is used as a description of a ‘range’ of notes.

When written, there is a distinction between the interval and the range of notes:
When a ” / “ is used between two notes, it is an interval.   A3/A4 is the interval of an octave.   The prime octave A3/A4.
When a ” – “ is used between two notes it is an ‘area’ or range of notes.   A3-A4 is the range of notes between and including A3 and A4.

A2/A3 is an interval, A2-A3 is the range of notes between and including A2 and A3.

A2/A4 is an interval, where as A2-A4 is the range of notes between and including A2 and A4.