# Periodic Cicadas are Coming: Mathematical Bugs in the Prime of their Lives

They emerge from the ground every 13 or 17 years.

ByABC News
April 18, 2016, 5:51 PM

&#151; -- Another 17 years have passed for one brood of periodic cicadas -- the time has come for billions to emerge from the ground in deafening drones. But they aren't just unusually loud, they're curiously into math. Periodic cicadas only have life cycles of prime numbers.

The mysterious life span of 13 or 17 years are prime numbers -- only divisible by themselves and one. This fact has both scientists and mathematicians looking for theories to explain the phenomenon.

One idea shared by both sides is that the prime life cycles do not align with the life cycles of the cicadas predators, protecting the broods of cicadas from extinction.

“Cicadas want to surprise their predators,” Glenn Webb, a mathematician at Vanderbilt University who has studied and wrote about the life cycles of cicadas, told ABC News today. “They swamp and overwhelm their predators, as part of their strategy to survive.”

Webb first became interested in studying the life cycles of cicadas when he moved to Nashville “a long time ago” around the time of a cicada emergence. “I remember in my yard there were so many of these cicadas. You couldn’t walk across the driveway without one crashing into you,” he said.

The birds began feasting on the cicadas a few days after their emergence, and the birds’ stomachs began to balloon. Webb wondered how the cicada broods would be able to populate so much without becoming extinct from their predators.

He created a study in which he chose non-prime numbers, such as 10, 12 and 15, for the life cycles to see if the cicada population would be at a disadvantage. At those intervals he found that the cicada population would be “annihilated or significantly reduced.”

The periodic cicadas are not to be confused with annual cicadas, which come out every summer. Periodic cicadas emerge only in the Spring, every 17 years in the northern region of the U.S., and every 13 years in the Midwest and South. Ground temperature must exceed 64 degrees Fahrenheit.

When they arrive in a massive brood, they mate for about four to six weeks. The adults produce eggs and die, while the nymphs go underground to grow and develop. The cicadas are harmless to the environment, except for breaking some branches or cutting through leaves on trees when the females lay their eggs.

This year, Brood V, which consists of three different species -- Magicicada septendecim, M. cassini, and M. septendecula -- will be emerging in areas of New York, Maryland, Ohio, Pennsylvania, Virginia, and West Virginia. Scientists predict their numbers to reach the billions.

“It’s interesting that there’s three species synchronized in the 17 year broods and four species in the 13 year broods,” Lou Sorkin, entomologist at the American Museum of Natural History, told ABC News.

There are approximately 15 broods of periodic cicadas, and they all are synchronized on 13 and 17 year life cycles. “No other species has as synchronized of an emergence,” he added.

Sorkin explained that the cicadas probably evolved during the glacial retreat across North America in the Pleistocene epoch, around 1.8 million years ago. They likely emerged above the ground when it became warmer. He believes it was probably natural selection that helped the 13 year and 17 year broods survive. Other broods and species probably became extinct because predators evolved with them.

Esteban Tabak, a mathematics professor at NYU, sees the synchronization of the cicadas as an example of the theory of resonance.

He explained it using the example of a swing -- the more you push the swing the more regular intervals there will be. If the pushes are happening regularly enough that they start to match the life cycles of their predators, the cicadas will be pushed to extinction. “The cicadas don’t want to be pushing any swing,” Tabak told ABC News. “What’s the way to do that? Well it’s hard. How do you not push any of them? That’s where the prime years come from.”

Different theories have been proposed by scientists and mathematicians. Webb says there is no one consensus about the meaning of the prime number life cycles -- or whether there is any reason at all. He believes that that they make not any difference for the periodic cicadas.

“My theory does add up,” he said, adding that these insects are difficult to study because their emergence is so infrequent. "Maybe someday they’ll be a clear answer, but right now it’s just a hypothesis.”