Close your eyes. You are a cicada nymph — pale, wingless, the size of a coffee bean — hanging in total darkness beneath an Illinois forest. You have never seen light. You have never heard rain. Your entire world is one tree root, and you have been sipping its thin, watery sap since the spring you hatched and burrowed down.
That was sixteen years ago. Presidents have come and gone above your head. Kids who were babies when you dug down are now learning to drive. And you have missed all of it — on purpose. Because you, little nymph, are running one of the boldest survival strategies mathematics has ever produced. You are a Magicicada, a periodical cicada, and your whole species has bet its existence on a single idea:
Hide for a prime number of years. Then all come up at once.
There are seven species like you in eastern North America — three that wait 17 years, four that wait 13. Both numbers are prime: divisible by nothing but 1 and themselves. That is not a coincidence. That is the whole trick — and in a moment, you'll get to discover it yourself.
You have no calendar. No clock. No light to mark the days. So how do you know when seventeen years have passed? Scientists puzzled over this for decades, and the answer turned out to be delicious: you count springs by taste.
Every spring, when the tree above you unfurls new leaves, the sap in its roots briefly turns rich with amino acids — a once-a-year surge researchers nicknamed the "spring elixir." Down in the dark, you feel it arrive through your feeding straw like a bell ringing: that's one. Somewhere in your body, a tally goes up.
In 2000, ecologist Richard Karban and colleagues proved it with one of the sneakiest experiments in biology. They took 15-year-old nymphs from a 17-year brood, settled them on potted peach trees — and then tricked the trees into blooming and leafing twice a year. The cicadas dutifully counted the sap surges, hit "seventeen" in half the time, and emerged a year early. They weren't counting years at all. They were counting flushes.
Watch two nymphs count. One lives under an honest tree; one lives under a tree forced to bloom twice a year.
Here is your enemy: not one predator, but cycles of them. Bird and small-mammal populations boom and crash on rhythms of their own — a boom every 2 years, every 3, every 6. Emerge in a boom year and your family is an all-you-can-eat buffet for a predator army at full strength.
So: if you could choose any cycle length, what should it be? Drag the sliders. Orange bars are your emergences; blue bars are predator boom years; a red ✕ means you surfaced straight into the jaws. The math doing the work here is the least common multiple — the first year two cycles collide.
Biologists Monte Lloyd and Henry Dybas first framed this predator-dodging idea in 1966, and Stephen Jay Gould made it famous in his 1977 essay “Of Bamboos, Cicadas, and the Economy of Adam Smith.” In 2001, physicists Eric Goles, Oliver Schulz and Mario Markus even built a predator–prey computer model in which the surviving prey cycles evolved into primes on their own. (Other scientists suspect the ice ages and the risk of mismatched hybrid offspring helped lock the numbers in — in real forests, several pressures can push the same direction.)
Seventeen tallies are in. Now you wait for one final message: heat. When the soil eight inches down holds steady at about 64°F (18°C), usually on a soft evening after rain, every nymph in the forest gets the same signal on the same night. You have one job now: climb.
Drag the temperature up and watch what one warm May evening unleashes. This is the other half of the strategy — predator satiation. No single cicada can fight off a blue jay. But a million per acre, all at once? The predators eat until they literally cannot eat any more… and barely dent the crowd.
Sound is off until you press the button. A real chorus of Magicicada cassini can hit ~100 decibels — males singing together to out-shout the entire forest.
One last piece of prime magic. The 13-year broods and the 17-year broods are both ticking away in the same continent — so how often do two particular broods surface in the same spring? Since 13 and 17 share no factors, the answer is 13 × 17 = 221 years.
Watch the two cycles spin. Each dot completes one lap per emergence. They only line up at the top once every 221 years:
It last happened in 1803 — the year Thomas Jefferson signed the Louisiana Purchase — when Brood XIX (the 13-year “Great Southern Brood”) and Brood XIII (the 17-year “Northern Illinois Brood”) rose together. Their next shared spring came in 2024: over a trillion cicadas across the Midwest and South, with the two broods brushing shoulders in a sliver of central Illinois. Miss it? The next appointment is 2245.
Tap a year to see who was scratching their head about you.
Seventeen years of study comes down to this. Pass, and you've earned your wings.
Two players, one hallway of 30 floor tiles (or 30 numbered papers). The predator secretly picks a boom cycle from 2–6 and stands on every multiple of it. The cicada picks an emergence cycle from 10–20 and walks the line, stepping only on their own multiples. Every shared tile costs the cicada a point. Play three rounds, then swap. You'll feel the theorem in your feet: prime cycles barely ever land on an occupied tile. Then check the champion: why do 13 and 17 beat 12 and 15 every single time?