TITLE: Does there exist infinitely many prime knots?
QUESTION [7 upvotes]: 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.)

REPLY [2 votes]: Yes.
Kauffman and Lopes found some very elementary families: https://arxiv.org/pdf/1604.02510.pdf .