Periodical cicadas in the genus Magicicada have unusually long life cycles for insects, with periodicities of either 13 or 17 years. Biologists have explained the evolution of these prime number period lengths in terms of resource limitation, enemy avoidance, hybridization and climate change. Here, I question two aspects of these explanations: that the origin of the life cycles was associated with Pleistocene ice age events, and that they evolved from shorter life cycles through the lengthening of nymphal stages in annual increments. Instead, I suggest that these life cycles evolved earlier than the Pleistocene and involved an abrupt transition from a nine-year to a 13-year life cycle, driven, in part, by interspecific competition.