Do you have any evidence of the higher incidence or prevalence of prime numbers in nature, other than happen-stance or co-incidence?

I believe you're mistaken in claiming that prime numbers are used in nature. I would simply state that prime numbers occur in nature; numbers occur in nature and must be used to describe natural phenomena and it is a mere coincidence that some numbers which occur are primes.

While it may be true that the cicada emergence cycle happens to be a prime number, is it always exactly so, or in some cycles is it an even number? What about other insects or varieties of cicadas that may use a non-prime number yearly cycle? As in the examples stated above, humans have twenty-three pairs of chromosomes, chimps have twenty-four. That chimps have 24 pairs does not make the human's 23 pairs less prime, just more likely to be co-incidental. It would appear that the majority of the comments and answers to this question are joke answers, and perhaps this question should be closed if joke answers are the only answers which mathematicians can provide.

If you could come up with a mechanism to collate all of the occurences of numbers in natural phenomena as a multi-set $S$, and then show somehow that the prevalence of prime numbers in this multiset $S$ is greater than would be expected by chance for another randomly selected multiset over the integers $\mathbb{Z}$, then perhaps I could buy the argument that primes are a sign of intelligence in nature.

The argument about SETI searching for prime number like signals from beyond is about the expectation that intelligent creatures would transmit a signal that would appear out of the ordinary and as a non-natural phenomenon. I think it's ridiculous to mix that up with looking for prime numbers in nature (and then jumping to the conclusion that some sort of intelligence or design might be behind it). Natural phenomena, even emergent evolutionary phenomena, have the statistical properties which they have.

Do you have any evidence of the higher incidence or prevalence of prime numbers in nature, other than happen-stance or co-incidence?