Mathematical models are presented to argue for the significance
of prime number emergences of 13 year and 17 year periodical cicadas (Magicicada spp.). The prime number values arise as resonances of emergences with
2 and 3 year quasi-cycling predators. Predators with 2 and 3 year quasi-cycles
are present due to their age dependent fecundity and mortality rates. Their
quasi-cycles are enhanced by the predation of cicadas during emergences and
thus exert significant influence on the cicada periodic life cycles.