Basically what the title asks.
All the other colors of the rainbow are either primary or secondary. Violet is a shade of purple and (as I’ve always understood it) indigo is somewhere between navy and purple.
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It’s cultural courtesy of Isaac Newton, who took the infinite spread of colors from a prism and assigned them seven names, seven being an auspicious number. He could have omitted orange or added cyan just as easily. For purposes of the color spectrum indigo and violet are both pure colors with a single wavelength. Artistically you are correct, they are both mixtures of red and blue.
Nature blurs the line a bit with rainbows, which typically have a very faint secondary rainbow just inside the primary. You might not even see it, but the brightest bit of the secondary (red) overlaps with the blue of the primary and makes it look a little purpleish, even as the rest of the secondary fades to nearly invisible.
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