When people talk about bright colors they often call them “primary colors”. But to the artist and the color professional there are only three primary colors; red, yellow and blue. From these three colors, all other colors can be mixed, which is why they are called “primary”. The secondary colors (obtained from mixing one primary with another) are orange (red and yell0w mixed), green (blue and yellow mixed) and violet (blue and red mixed).
In the real world of mixing paint, it takes more than just one or two pigments to make every other color in existence. The reason is that each pigment whether natural or human-made is rarely “purely” a red, yellow or blue. And, the carrier or “base” solution the pigment is in can affect how the color appears.
In the art world, the carrier or base solution could be oil, acrylic, gum arabic (for watercolors), etc. In the world of house paint, a base is “tinted” (it has a color) and is different depending upon what type of house paint it is (interior, exterior, semi-gloss, eggshell, etc).
Color mixing can get pretty complicated.
But that’s nothing to worry about. Any professional paint store employee has a computer to help out with the color mix, and the most well-trained staff understand the science of mixing so that they can be sure the computer gets it right.
So…if you want to say, “Primary colors,” to define brights, that’s fine, most every color professional will visualize the usual Sesame Street kid’s colors and know what you mean.