Do cicadas know mathematics?

You know what 2020 is missing? An invasion of trillions of screaming cicadas after 17 years underground! Yes, seriously.
2020 is the year of “Brood IX”, a horde of more than 1.5 million cicadas that have been waiting underground for their big moment to emerge in some US areas and it has already started.
But before you start wondering if 2020 is really the end of the world, then rest assured this curious event is actually pretty normal.

Magicicada is the genus of the 13-year and 17-year periodical cicadas of eastern North America.
In the spring of their 13th or 17th year, mature cicada nymphs emerge in the springtime at any given locality, synchronously and in tremendous numbers.
After spending 17 years underground, millions of cicadas will emerge in parts of the United States.
This year periodical cicadas are expected to come out in early summer across southwest Virginia, parts of North Carolina, and in West Virginia. The last time the cicadas emerged in many of those regions was in 2003 and 2004, and as many as 1.5 million of the insects can emerge per acre of land.
Periodical cicadas are some of the longest-lived insects in the world, despite they spend almost their entire lives underground and, according to Virginia Tech university, they live in the soil and feed on tree roots for periods of either 13 or 17 years depending on the species.
Periodical cicadas are grouped into geographic broods based on the calendar year when they emerge. For example, in 2014, the 13-year brood XXII emerged in Louisiana and the 17-year brood III emerged in western Illinois and eastern Iowa, with Brood IX (nine) emerging this year as part of their 17-year cycle. When the nymphs are ready, they build mud tubes, called a cicada hut, in the soil and crawl out to find a place to moult into their winged adult form and to mate.
They only live for two to four weeks as adults, but during that time can cause significant damage to young trees, as well as to vines and saplings where females lay enormous quantities of eggs. The male cicadas are also very loud, “singing” by vibrating membranes on their abdomen to court females. Each brood, or generation, even has it’s own unique song that the males sing to attract females. And by sing, I mean screech at 90 decibels, which is about the loudness of a dirtbike or a lawnmower. So romantic….

Why the insects emerge on those specific intervals remains unclear, though some researchers think it could help them avoid predators. 13 and 17 are prime numbers, meaning they can’t be divided evenly by any other number except one. If cicadas came out every 16 years, for example, predators with two-, four, and eight-year life cycles would be around that year to eat them. This is a curious area where life science and mathematics intersect. The math comes in the form of a problem that the cicadas need to solve: how do you survive to reproduce before being eaten by predators?
For some kinds of cicadas, the answer lies in adaptations. For example, some cicadas are fast fliers, while other species use camouflage to hide from predators. But the 13- and 17-year cicadas don’t have any good defenses. They’re slow, easy to spot, and apparently very tasty. So having a prime numbered life cycle keeps you out of synch with the life cycle of predators, which prevents any particular kind of predator from being too dependent on the cicadas for food. In other words, if you’re a predator with a one-, two-, four-, or even eight-year life cycle, you’re not going to get too used to catching cicadas that show up only once every 13 or 17 years.
There is also a species of cicada that emerges every year, called dogday or annual cicadas.

In 1898, entomologist C. L. Marlatt assigned Roman numerals to 30 different broods of periodical cicadas: 17 distinct broods with a 17-year lifecycle, to which he assigned brood numbers I through XVII (with emerging years 1893 through 1909), and 13 broods with a 13-year cycle, to which he assigned brood numbers XVIII through XXX (1893 through 1905). Many of these 30 broods, however, have not been observed, and two of the brood numbers assigned by Marlatt (broods XI and XXI) existed at one time, but have become extinct. The Marlatt numbering scheme has been retained for convenience (and because it clearly separates 13- and 17-year lifecycles), although today only 15 broods are known to survive.