The prime numbers have nothing to do with predators. Predators require regular feeding from live prey. A prey species that hides for even one year causes sign

The prime numbers have nothing to do with predators. Predators require regular feeding from live prey. A prey species that hides for even one year causes significant starvation in predators that could otherwise come to depend on it. This effect is maximized after only a handful of years of hiding. No lizard or bird could survive on stored fat for more than one or two years. The prime numbers come from competition between strains of cicadas. First consider that genetic timers are not perfect: most cicadas may emerge after N years, but a fraction will emerge in N-1, N+1, or even farther years due to randomness in genetics and the environment. By blind chance, occasionally an early group will become plentiful, causing a predator population boom that smashes the population of the "correct" year. It's like a badly-made gear that occasionally jumps one tooth forward. Second consider what such jumping does to strains that are not relatively prime, such as 6 and 12 year cicadas. Eventually the random chance effect will synchronize them so that they emerge in the same year. Because these year skipping cicadas all evolved from the same parent species, they will be closely related. This creates a cross-mating problem if they emerge at the same time, causing matings to either produce no offspring, or to produce hybrids that are synchronized with neither period. There may also be problems with excess damage to the host plants. Therefore evolution favors strains that synchronize as infrequently as possible. That means prime numbers. IIRC a few years back some scientists created a simulation with plausible numbers for fertility and hybrids, and the result was spontaneous emergence of the prime number periods for the observed strains of cicadas. Edited for clarity.