In addition to this, there will always be 2 sets of "primary" colors for a given eye: Additive and Subtractive.

Additive primary colors are necessary when you have no light, and need to create color. Think a black screen, and you are creating colors with RGB pixels.

Subtractive primary colors are necessary when you have full-spectrum (white) light and need to filter down to a single color.

Other "primary" colors, such as the red, blue, yellow pigment primaries we learned in Kindergarten exist because pigments historical couldn't be created perfectly, and those "primaries" are the best way of getting the most colors, but still have a very limited (by comparison) gamut.