Why do periodical cicadas emerge on prime-number cycles?

The answer

Periodical cicadas of the genus Magicicada spend either 13 or 17 years developing underground, feeding on tree root sap, before emerging simultaneously in enormous numbers. Both 13 and 17 are prime numbers, which mathematicians have shown minimizes the overlap with predator population cycles; a predator with a 2, 3, 4, 5, or 6-year cycle would rarely synchronize with a 13 or 17-year cycle. The mass emergence itself is a survival strategy called predator satiation: by appearing in billions simultaneously, cicadas ensure that predators become overwhelmed and cannot eat them all, guaranteeing enough survivors to reproduce. Their emergence is triggered by soil temperatures reaching exactly 64 degrees Fahrenheit (18 degrees Celsius) at a depth of 8 inches.