Prime number theorem for knots?

Question

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 $$ \pi(x) \sim \frac{\log(x)}{x} \; \mathrm{?}$$