Trey Jones wrote:

Even primes seem abstractly possible..

In fact, it's already been demonstrated theoretically.

Prime numbers can be generated "naturally" from some simple assumptions about predator-prey population dynamics.  It's already been found that a few species of cicada insects appear every 7, 13 and 17 years.  There is a conceptual evolutionary advantage to having a prey population flourish at periods which are prime numbers; that prevents a predator population from evolving to flourish at regular intervals to prey on them.

http://alpha01.dm.unito.it/personalpages/cerruti/primality/biological-primes.pdf