Why do cicadas emerge in huge numbers after years underground?

Periodical cicadas are famous for spending 13 or 17 years underground before emerging in enormous numbers. Once they surface, adults live only a few weeks, during which they mate, lay eggs, and die. The synchronized emergence is thought to reduce predation by sheer numbers, a strategy often called predator satiation. The 13- and 17-year cycles are prime numbers, which may help prevent predators from synchronizing their own life cycles to cicada appearances. These broods are among the most extraordinary life cycles in insects.