By definition, a prime lens is a fixed lens system with a fixed focal length.
Then, simple physics tells us that it should be able to focus only on one plane (at a fixed distance) in front of it. But in fact you can focus on objects near as well as far.
What am I missing here?
Answer
A prime lens still has a moving focus element allowing you to change the focal plane through the range of the focusing ring's range. A prime is a lens that has a fixed focal length (100mm, 50mm etc) as opposed to a zoom which will allow you to cover a range of focal lengths (70mm-200mm for example).
A fixed focus lens cannot change its focal plane, but this is not the same as a prime lens.
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