Watch as David Attenborough signals his interest in mating with a male cicada. Scientists think that cicadas have 13- or 17-year mating cycles because, being prime numbers, those periods are not divisible by those periods of potential predators. From Stephen J. Gould:
Many potential predators have 2-5-year life cycles. Such cycles are not set by the availability of cicadas (for they peak too often in years of nonemergence), but cicadas might be eagerly harvested when the cycles coincide. Consider a predator with a life-cycle of five years: if cicadas emerged every 15 years, each bloom would be hit by the predator. By cycling at a large prime number, cicadas minimize the number of coincidences (every 5 x 17, or 85 years, in this case). Thirteen- and 17-year cycles cannot be tracked by any smaller number.
It's a bit more complicated than that, but Gould's argument covers the basics. (thx, @mwilkie)
Responding to a query from an NPR science correspondant about prime numbers, Hoefler & Frere-Jones researched the lengths involved when typesetting the largest known prime number, which has almost 13 million digits.
Joe liked the idea of measuring how long this number would be if it were set in type, which immediately called into question the choice of font. The number's length would depend chiefly on the width of the font selected, and even listener-friendly choices like Times Roman and Helvetica would produce dramatically different outcomes. Small eccentricities in the design of a particular number, such as Times Roman's inexplicably scrawny figure one, would have huge consequences when multiplied out to this length. But even this isn't the hairy part. Where things get difficult, as always, is in the kerning.
In some cases, properly kerning the number resulted in a difference of more than 1000 feet for 12 pt. text.