Finding primes in signals is seen as a sign of some kind of intelligence - see e.g. the role of primes in the search for extraterrestrial life (see e.g. here).
This is because there are relatively few examples of numbers that appear in nature because they are prime. One example of the use of prime numbers in nature is as an evolutionary strategy used by cicadas of the genus Magicicada (see e.g. here or here: )
Do you know of any other instances where prime numbers occur in nature? Could you please also give a source/link - and perhaps some background. Thank you.
 Goles, E., Schulz, O. and M. Markus (2001). "Prime number selection of cycles in a predator-prey model", Complexity 6(4): 33-38
Edit: Obviously many people misunderstood me. I didn't mean the occurrence of prime numbers just by coincidence - but because they are prime. The cicadas example - although being controversial - at least hints at some kind of evolutionary strategy.