To many, the prime numbers are a foreign and useless concept conjured up in the laboratories of decrepit mathematicians, having little to no impact on their lives other than some nebulous relevance in some form of encryption or computing they read about in the news. This couldn’t be further from the truth. Once every seventeen years, prime numbers become very relevant very quickly to millions of people across America. An unavoidable swarm of insects fills the sky for weeks on end, chirping collectively up to 100 decibels. This year, like 2004, and many more years before it, pharaoh cicadas are breeding and swarming in their billions.
Pharoah cicadas are often referred to as the 17-year locust as they pass the majority of their surprisingly long lives underground as wingless “nymphs”. Theories vary as to how they know how much time has passed; perhaps they possess an internal molecular clock or can detect changes in tree sap underground. Regardless, when that seventeenth year finally does come, they all grow wings, rise from their slumber, eat, breed, fly and then die. In all, they live for about six weeks as flying cicadas, ensuring the survival of their genes and fluttering off this mortal coil, leaving behind a wake of destruction and irritation across the northeast of the US.
Why 17 years? What is so special about this number that it controls the lives of millions of individual creatures? The answer is simple. It is a sufficiently big prime. The 17-year breeding cycle is large enough to protect the species from excessive predation. For a predatory species’ breeding cycle to overlap, it would have to breed either every single year or every seventeen years. Any other number would mean that it coincides at most 50% of the time. When they do overlap in a certain year, the cicadas will be vulnerable to predators as they swarm in their masses. However, any increase in predator population will be countered during the next cycle as the plentiful source of food will have disappeared. Birds and small mammals that feast on these cicadas will need to find food elsewhere for the intervening 16 years. Thus both the cicada and predator population remains stable despite huge quantities of available food every 17 years.
The evolution of this trait is perfectly governed by Darwinian theory. Species of cicada that lived underground for longer, and especially for a prime number of years, survived better and bred more, outsurviving their less fortunate cousins. Whether this pattern is purely genetic or partially learned behaviour remains to be discovered and is likely linked to the other missing detail of how they keep track of time. However, the number 17 is not unique given that we are aware of the existence of 13-year and other similar sized prime number breeding cycles.
Those people unfortunate enough to be living in New York at the moment 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 that is guaranteed to be much much less fun. Whilst they may be annoying, their story is incredible and shows that prime numbers aren’t just an irrelevant concept but critical to the survival of billions of creatures.