Gray is not. Sir Isaac Newton was the first to discover that all shades of
white are a mixture of fundamental colours, the now called spectral colours.
This is not related to the choice of colours for printing or photographs,
several choices could do the job, the RGB (by addition) or the one
used by a subtractive process may have several equivalent choices,
although not practical, so any colour could be a primary colour
in this case.
A pure colour, or a spectral colour, that is how I intend your question,
deals with the frequency (spectrogram with only one spike) of the light
that gives us that perception.
For any shade of gray you will need at least two colours, that is at least two spikes in the frequency spectrum, so it is not a pure colour.