Cicadas with 13- and 17-year life cycles emerge less often with other broods than do the ones whose cycles are non-prime numbers. For example, when a brood with a 14-year life cycle emerges, it will share the summer with two-year and seven-year broods, with which it will interbreed and produce mongrel offspring. A 16-year brood will share a mating season with two-, four- and eight-year broods, and an even more diverse group of hybrids will result.
In contrast, when 13- and 17-year broods are out, they share the season only with broods having short life cycles (such as one, two or three years) -- and life cycles that short presumably couldn\'t survive the Pleistocene climate. The net result was that 13- or 17-year cicadas didn\'t have their genes \"diluted\" by hybridization -- except every 221 years, when they were out together in the few places where they shared the same turf.
Of course, periodical species didn\'t pick 13 and 17 as their magic numbers. As with all evolutionary processes, choice played no part.
What happened, instead, was that broods of other cycle lengths simply became extinct. They emerged in a cold summer and failed to reproduce, or they emerged in insufficient numbers and were eliminated by predators. What remained were the broods mathematically most likely to make it across the Pleistocene minefield -- 13 and 17. Furthermore, in those populations synchronicity was essential. Individuals whose timing was off just a little -- ones that emerged a year early or late -- were extirpated. But their brethren whose genes endowed them with perfect timing generation after generation, survived.