Color vision and stimulus is not a straightforward mapping of primaries triggering cones. If it were that simple you could trivially render all perceivable colors with 3 chosen primary colors. This is impossible to do. You can mathematically define 3 primaries that cover the entire visible spectrum but they cannot physically exist (complete, but imaginary). Any chosen set of 3 primaries is a compromise. For subtractive materials it is trickier, which is why photo inkjet printers will use up to 8 primaries.
You might find this informative: https://web.archive.org/web/20080717034228/http://www.handpr.... The section starting with Maxwell and the "3 artist's misconceptions" especially.
But the only general definition of primary is basically just any set of colorants that can be mixed to get a useful gamut. In subtractive materials, this is why you won't see a painter messing around with mixing cyan, magenta, and yellow (better explained in the link).