Sailesh Ganesh reminded me that I haven't posted a solution to my Cicada question, posed here ten days ago. Why does Magicicada septendecim have a life-cycle as long as 17 years, and what's the significance of the 17?
As I indicated there, I read about this in Simon Singh's "Fermat's Last Theorem." Here's a paraphrase of his explanation:
It's likely that the cicada has a parasite that also has a long life-cycle. Now let's say the parasite's life-cycle is two years long. Any cicada life-cycle that is an even number of years long means the parasite and cicada will "meet" regularly, with disastrous consequences for the cicada. What if the parasite had a three-year life-cycle? Then the cicada must evolve to avoid life-cycles that are multiples of three years long.
Continue with this reasoning, and you see that the cicada's best option is a life-cycle that's long, and prime. Like 17 years. Now, if the parasite has a two-year cycle, cicada and parasite will meet every 34 years. If the parasite has a longer cycle, they will meet even more rarely: if it has a 16-year cycle, onle every 272 years (16 x 17 = 272).
Only two cycle-lengths will make these meets more frequent: a one-year cycle and a 17-year cycle. But if the parasite has a one-year cycle, it will have to live out its life 17 successive times without the cicada to feed on. Not a likely option. If it has to evolve to a 17-year cycle, it would first have to evolve to and through the 16-year cycle, and that means there will necessarily be one of those 272-year gaps.
Both ways, the cicada's long prime life-cycle is its protection.
I tell you, primes are a delight.