Cicadas incubate underground for long years. They emerge every 13 or 17 years to mate and make annoying noises when people are trying to sleep. Both 13 and 17 are prime numbers. What is it that makes cicadas come out during these years?
Cicadas spend so long underground that it hardly seems worth it for them to come out at all. They're almost totally adapted to life underground, sipping the juices from plant roots and tunneling around in the mud. When they do burst out into the sunshine, they are fully prepped for it. They're able to fly, and mate, and then they quickly die off, leaving a feast for birds, small mammals, and larger insects. Plenty of animals change environments to mate, but the cicada stands out for its long incubation period and its suspicious number of years in between. Both cicada cycles are prime numbers, only divisible by one and itself.
For a long time, these prime numbers were thought to be coincidence, until Stephen Jay Gould advanced a theory that they were driven below ground so often to escape their predators. They go to such extraordinary lengths because evolution is a long-term game. If the cicadas emerged every ten or fifteen years, their emergence would coincide with predators whose life-cycles neatly divided into theirs. The ten year cicadas would be preyed on by creatures which had a one, two, five, and ten year life-cycle. The fifteen year cicadas would fall victim to any creatures with one, three, five, and fifteen year cycles. Although these predators would not feast on cicadas every generation, they would manage to eat well every third to fifth generation.
As it is, the three year animals would only meet up with the seventeen year cicadas every 51 years, or seventeen generations. An animal species might develop a habit of preying on cicadas if it met up with them every few generations. Perhaps those members of the species which experienced a boom in the reproductive cycle every few generations would be favored. Fifty-one generations would be a tougher row to hoe. Perhaps the thirteen and seventeen year cicadas made it this far because, due to their prime-number loving ways, no other animals were able to sync up with their reproductive cycle.