It makes sense that an animal might hid away in the ground while it's maturing, but 17 years is a long, seemingly random amount of time. But it's not like cicadas picked a number out of a hat and were stuck with it. There's a something specific about that number, and numberphile is sussing it out.
It's crazy to think, but it turns out cicadas are actually doing math through natural selection, and hunting down the prime numbers as to be eaten as infrequently as possible. Of course, if I had an incentive like that, maybe I'd be better at math too.