I'm not a topologist and I just saw the definition of prime knot a while ago.

Today I'm somewhat supprised to realize that I don't even know if there are infinitely many prime knots? If this question is not completely trivial then I'm hoping to see a "proof from the book".

(A related question is, is the decomposition of a composite knot into prime knots unique? I would hope so but I don't have a strong reason to support that.)