Periodical cicadas spend thirteen or seventeen years underground drinking from tree roots, then come up all at once, by the billion, for a few weeks of noise. Both numbers are prime, and the favourite explanation is that this is no accident: a predator whose numbers boom every two, three, four or six years keeps missing them, and broods on different primes rarely surface together to interbreed. The thirteen- and seventeen-year broods that met in Illinois in 2024 had last done it in 1803, and won’t again until 2245. The cicada, of course, has no idea what a prime is. It seems to count by the tree: in one experiment, trees coaxed into leafing out twice a year brought their nymphs up a year early. So if the idea is right, the arithmetic was never in the insect. It’s in the long record of every brood that came up on twelve, or fifteen, or sixteen, and met something waiting. A number known mainly for what won’t go into it, kept by an animal a tree can fool.