TITLE: Generating prime knots (in order)
QUESTION [6 upvotes]: In this really cool paper https://arxiv.org/abs/1612.03368, A. Malyutin shows that the probability that a random prime knot of up to $N$ crossings (as $N$ goes to infinity) is not generically hyperbolic (mod some "standard conjectures"). Now, the question is, how would one go about generating prime knots, either in order of crossing number (preferred) or in some randomized way? It is an interesting question of which conjectures are actually not correct (since, just like HRJW in the comments, I believe that a random prime knot should be hyperbolic).

REPLY [4 votes]: I'm not sure this is what you are looking for, but Adams et al. (https://arxiv.org/abs/1208.5742) show how every knot is obtained from a permutation in $S_n$. We sampled random permutations and used SnapPy to determine the resulting knot types, and they seem to be generically hyperbolic (https://arxiv.org/abs/1711.10470, Figure 14).