According to the color theory, two complementary colors are the most distant ones on the color wheel and own a high contrast, e.g., Red and Green.
For the primary colors, Red and Green are complementary colors, but blue is not complement with them. In this case, are the primary colors the most contrasting colors?
Red and green are complementary colors on that old color wheel, an RYB model targeted for painters, where Red, Yellow and "Blue" are the primary colors. Also, they are complementary colors in a Lab* model.
A modern color wheel uses RGB as primary colors and CMY as secondary or vice-versa, CMY as primary and RGB as secondary.
In that model, Red is complementary of Cyan.
So, if they are opposite, yes, they have maximum contrast but only in hue. There are several types of contrast. We also have brightness contrast.
Although we have some color models like HSB or HSL where one component is brightness, in this case all the hues have the same brightness because it only interprets it as a series of numbers.
So we have to interpret the brightness component as a perceptual brightness.
In this case, I am converting the image to Grayscale using a typical conversion.
You now can see that the maximum brightness difference is between yellow and blue.
So in the case of an RGB-CMY color wheel, the maximum contrast is Blue-Yellow.
But we can also consider that black and white are the most contrasting colors taking only in account brightness.
But we also have saturation contrast.
If we have then one color saturated and one not, one bright and the other not, the most contrasting colors are considered yellow and black. That is why it is used on (non-warning or informative) road signs and school buses.
This question is a bit broad (and sounds a lot like homework!), but I'll give you a couple of pointers that should help in your research...
There is more than one colour wheel and more than one corresponding set of primary colours. You seem to be mixing them up in your question. Red, Green and Blue are the primary colours for RGB and in RGB Red and Green are not complementary colours. Red and Cyan are complementary colours, cyan being Green plus Blue. Similarly, the complementary colour for Blue is Yellow (Red plus Green). To get a better understanding of this try searching for "RGB Colour Wheel" or look into the difference between additive and subtractive colour models.
Also, contrast would more usually be used to describe a difference in brightness so the 'most contrasting colours' would be black and white. Although some people wouldn't count them as colours at all. What you seem to be describing is a a contrast in hue. The most contrasting colours in these terms would always be complementary colours for the given colour model.
Like I said, the question is a bit too broad for this format, but hopefully this answer will set you in the right direction.
In short contrast is another feature of the color like hue,or luminescence but contrast is more complex,its a function that calculate how much difference in luminescence between two colors, Contrast=(color A Luminescence - color B Luminescence) so red or green have different hue,maybe same or different luminescence , so what i mean these are properties that describes how the color gonna be..
Are the primary colors (red, green, and blue) the most contrasting colors?
No. Pure white and pure black are the most contrasting two colors.
When speaking about colour theory, the twelve-hue colour wheel (Chromatic Diagram) suggested by Michel Chevruel in 1865 is the one usually referenced. This layout allows theories about simultaneous contrast and various harmonies to be created. It is the "classic" colour wheel used in basic and introductory colour theory. It is the one you link to (without a credit.)
His layout puts Red opposite Green, purple opposite yellow, and blue opposite orange (simultaneous contrast).
Chevruel had an edge. Not only was he a chemist; but, also a painter with a critical eye and a drive to formulate stable vibrant pigments.
