Red pigments usually have a “PRXX” designation, where “PR” means “Pigment Red”, and the Xs are digits which correspond to a certain chemical substance (or range of similar substances). Purple colors can have “PR” or “PV” (“Pigment Violet”) designation.
Below, you will find the swatches of all the various reds that I have or had in my possession. Swatches have two areas, the upper one to demonstrate the range of tints (diluted paint), and the lower one to show the mass-tone (the paint taken straight from the tube without diluting or, in case of the pans, the thickest concentration I could get). On each swatch you will notice a black line – I made it to give the idea about the transparency of the paint.