Are knot complements prime 3-manifolds?

Question

Well, that is basically the question. Is the complement of a knot, i.e. an smoothly embedded copy of $S^1$ in $S^3$ a prime $3$-manifold?

Here I mean by prime:

A connected $3$-manifold $M$ is prime if there is no decomposition as a connected sum $N_1\# N_2$ of two manifolds neither of which is the $3$-sphere $S^3$.

Answer 1

By Alexander's Lemma, knot complements are irreducible $3$-manifolds, hence also prime manifolds, see here.