Prime Sequences in Nature

Question

I've heard that prime numbers are considered to be important in the field of cryptography, however are there instances in nature where prime numbers emerge?

I wonder if there any examples in nature where sequences of primes emerge?

Answer 1

There is a genus of cicada, Magicicada, whose members wait underground for either $13$ or $17$ years before emerging en masse. There are different theories as to why this is so, but it is generally accepted that the prime-numbered periods are not coincidental, since they ensure that the two groups will not emerge at the same time except every $13\cdot17=221$ years.

From the Wikipedia article on periodical cicadas:

The emergence period of large prime numbers (13 and 17 years) was hypothesized to be a predator avoidance strategy adopted to eliminate the possibility of potential predators receiving periodic population boosts by synchronizing their own generations to divisors of the cicada emergence period. Another viewpoint holds that the prime-numbered developmental times represent an adaptation to prevent hybridization between broods with different cycles during a period of heavy selection pressure brought on by isolated and lowered populations during Pleistocene glacial stadia, and that predator satiation is a short-term maintenance strategy. This hypothesis was subsequently supported through a series of mathematical models, and stands as the most widely accepted explanation of the unusually lengthy and mathematically precise immature period of these insects. The length of the cycle was hypothesized to be controlled by a single gene locus, with the 13-year cycle dominant to the 17-year one, but this interpretation remains controversial and unexplored at the DNA level.

Answer 2

Sequences of prime numbers are also connected with physics (hence with nature). "In recent years, a rapidly expanding body of work has been making unexpected, seemingly unrelated connections between the mysterious distribution of prime numbers and various branches of physics", see for example this archive. In particular, there is a strong connection to quantum mechanics.