Prime number theorem for knots?

Is there an analog to the prime-number theorem describing the distribution of the prime numbers among the integers: A theorem that describes the distribution of the prime knots, perhaps with respect to the knots with $k$-crossings? Or a distribution with respect to some other relevant knot parameter? I.e., is there any analog to $$\pi(x) \sim \frac{\log(x)}{x} \; \mathrm{?}$$

• OEIS has some info. – Arthur May 27 '18 at 23:36
• @Arthur: Thanks! Almost too many references, and no clear distribution formula I can see. But much to penetrate to be certain. – Joseph O'Rourke May 28 '18 at 0:06