What genus contains periodical cicadas with 13- or 17-year life cycles?

The genus containing periodical cicadas with 13- or 17-year life cycles is Magicicada.

Magicicada contains seven recognized species native to eastern North America: three with 17-year cycles and four with 13-year cycles. Most of a cicada’s life is spent underground as a nymph, feeding on fluids from tree roots. In its emergence year, a population appears above ground in enormous, synchronized numbers.

The 13- and 17-year schedules are not the same as saying every cicada lives exactly that long. These are characteristic developmental cycles for periodical cicadas, while many other cicada species have shorter or less synchronized cycles. The prime-number intervals may help reduce the chance that predators with shorter, regular life cycles can repeatedly match their emergence.

A common mix-up is calling these insects “17-year locusts.” They are cicadas in the true-bug order Hemiptera; locusts are grasshoppers in Orthoptera. Adult Magicicada usually live only several weeks after emerging, primarily to mate and lay eggs.