Most non-primary colors are combinations of two or more primaries, but others are their own pure single colors. I think Jacquard's Brilliant Orange is one.
The trouble I have with using only the primaries is that they "spread" at different rates (different molecules for each dye), so if I have (or wanted to have LOL) white space between my colors, there is often a "halo" of another color that extends into that white area. I have the hardest time with reds, for example, or browns; most of the reds tend to have yellow halos the way I mix them, and the browns often have turquoise halos.
That's one reason I like to have some of the pure colors of non-primaries, or at least mixtures of other colors.
Paula has a chart but I'm too sleepy to dig for it ATM; I'll try to remember to go hunting for it tomorrow unless Paula beats me to it.

It shows which colors are pure and which are combinations/mixtures of others.