In North America, Cicadas spend most of their lifespan as underground larvae known as nymphs. Depending on the species, they emerge en-masse as winged adults after either 13 years or 17 years. When this behaviour was originally discovered, it was noted that the developmental delay involved two prime numbers, 13 & 17.

Theories were proposed which assumed that the prime number yearly cycles were a way of attempting to avoid synchronisation with the life cycle of predators.

Although widely accepted, there are several problems with these theories. Firstly, the cicadas actually emerge in more or less the same (total) numbers every year, because their life cycle is not syncronised between all groups. In addition, no genetic evidence of a 'timing' gene has yet been found.

There is strong evidence that species somehow 'count' the number of elapsed years by detecting changes in the sap of the tree roots on which the larvae feed.(ref.)

Another puzzle is explaining how the behaviours developed over evolutionary time : One suggestion is that the timings began during ice-age disruption of the life cycles (ref.).

Nevertheless :

Explaining the evolution of such an unusual life strategy is one of the most difficult problems for biologists."

Further information University of Connecticut

Note: Cicadas in other regions, e.g. South America, do not appear to synchronise.