Prime Numbers in Nature: Cyclical Cicadas

Oscar Lawson

To many, prime numbers are a useless concept studied in maths and soon forgotten about, having no impact on the rest of our lives. While they do have some applications in computing and encryption, primes never seem to crop up in day-to-day life, remaining as “special numbers” that aren’t all that special. However, once every seventeen years, prime numbers become very relevant very quickly to millions of people across America, as an unavoidable swarm of insects fills the sky for weeks on end, chirping collectively at up to 100 decibels. This year, 2021, like 2004 and many other years before it, pharaoh cicadas are breeding and smarming in their billions.


Pharoah cicadas are referred to as the 17-year locust, as for most of their fairly long lives (for insects), they live, wingless, underground as “nymphs”. Theories vary about how they know how much time has passed, perhaps possessing an internal molecular clock, or detecting changes in tree sap underground, but one way or another they all grow wings in the seventeenth year, rise together, eat, breed, fly and then die. In all, they live for about 6 weeks as flying cicadas, ensuring the survival of their genes and then fluttering off this mortal coil, but not without causing chaos for a lot of the north-east US.


So why 17 years? This is a large enough prime number to be able to protect the species from excessive predation. Since 17 is prime, another species would have to breed either every single year or every seventeen years to overlap with the pharaoh cicada’s breeding cycle, as there are no other factors of the number seventeen. Therefore, although in the year when cicadas emerge and swarm in masses, they will be vulnerable to predators, any increase in predator population will be countered by the next time they breed because the plentiful food will have disappeared for 16 years. Birds and small mammals that feast upon the cyclical cicadas need to find other food sources for the intervening 16 years, and thus the population size remains stable despite huge quantities of available food every 17 years.


How this adaptation evolved mirrors Darwinian theory exactly. Sub-species of the cicada that live underground for longer, and especially for a prime number of years, survived better and bred more so their offspring followed this trend. Whether it is purely genetic remains to be discovered and is likely linked to the other unknown of how they keep track of time. What we do know is that although 17-year pharaoh cicadas are the most common, there are also instances of 13-year cycles, another example of a prime number protecting animals against predators. Those living in places like New York now may despise the noisy incessant buzzing of a billion cicadas, but once every 221 years there will be a bumper brood of both cycles and we can be certain that will be even less fun. They may be annoying, but their story is incredible and shows that prime numbers aren’t just a useless concept but, in some cases, vital to a species’ survival.

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