Every so often, in the eastern United States, a patch of forest that has been silent for nearly two decades suddenly deafens. From the soil emerge cicadas by the billion — red-eyed, clumsy, harmless insects — climbing the trees, shedding their shells, and filling the air with a shriek loud enough to rival a chainsaw. Within a few weeks they mate, lay eggs and die, carpeting the ground with their bodies. Then the forest goes quiet again for another thirteen or seventeen years. These are the periodical cicadas, and the numbers in that sentence are the whole mystery.
Counting the years in the dark
Most of a periodical cicada's life is spent underground as a nymph, sucking sap from tree roots in the dark. What is remarkable is the precision of the timing. In any given brood, virtually every individual emerges in the same year, having counted out either thirteen or seventeen years below ground — not twelve, not fifteen, not sixteen, but one of those two specific figures. Scientists believe the nymphs track the passing years by sensing seasonal changes in the trees whose roots they feed on, each cycle of the tree's growth marking another year, until an internal count reaches the trigger.
Entomologists organise these populations into numbered broods, each emerging on its own schedule in its own region — Brood X, Brood XIX and so on — so that in different years, different parts of the country get their turn.
Why a prime?
The truly tantalising feature is that thirteen and seventeen are both prime numbers — divisible only by one and themselves — and biologists strongly suspect this is no coincidence. The leading explanation concerns predators and parasites.
Most animals that might eat cicadas — birds, small mammals — go through population booms and busts on cycles of their own, often a few years long. Imagine a predator that peaks every two or three years. If the cicadas emerged on a cycle that shared a common factor with the predator's cycle, their mass appearances would repeatedly coincide with the predator's peak years, and they would be feasted upon each time. By emerging on a prime-numbered cycle, the cicadas minimise how often their emergence lines up with any shorter predator cycle. Seventeen shares no factors with two, three, four or five, so an emergence coincides with such predators only rarely. A prime interval is, in effect, a mathematical strategy for dodging the schedule of anything that wants to eat you.
There is a second, related idea: a prime cycle also makes it hard for two different cicada broods to interbreed and blur their carefully synchronised timing, since broods of thirteen and seventeen years only coincide once every couple of centuries.
And this brings us to the survival strategy that makes the whole spectacle work: predator satiation. Periodical cicadas have no defences to speak of. They do not bite, sting or hide. Their trick is overwhelming abundance. By emerging all at once in numbers so vast — often hundreds of thousands or even millions per acre — that every predator in the area can gorge itself and still barely make a dent, they guarantee that enough survive to reproduce. Coming out early or late, alone, would be suicide; the safety is entirely in the synchronised crowd.
In 2024 the phenomenon produced a rare event that drew wide attention: two major broods, one on a thirteen-year cycle and one on a seventeen-year cycle, were due to emerge in the same spring across overlapping regions of the American Midwest and South-east — a double emergence of the sort that only recurs after more than two centuries, because thirteen times seventeen is two hundred and twenty-one years. Trillions of insects were expected across many states, though the two broods largely occupy different areas and only brush against each other at the edges.
It is one of the strangest facts in nature that a small, red-eyed black insect should organise its entire life around a prime number. The cicada does not know arithmetic, of course. It simply inherited, over deep evolutionary time, a clock set to an interval that happens to be indivisible — and that indivisibility, blindly selected because it kept its ancestors alive, is why the forests of the eastern United States still explode into sound on a schedule you could set a very patient watch by.
Quiz nuggets
- Periodical cicadas emerge on cycles of either 13 or 17 years, both prime numbers, after living underground as nymphs.
- The prime-number cycle is thought to help them avoid syncing up with the shorter boom-and-bust cycles of predators.
- Their survival strategy is predator satiation: emerging in overwhelming numbers so predators cannot eat them all.
- Populations are grouped into numbered broods, such as Brood X and Brood XIX, each on its own schedule.
- In 2024 a 13-year brood and a 17-year brood emerged together — a coincidence that recurs only every 221 years (13 × 17).