Cicadas are flying, plant-feeding insects similar to leafhoppers and scale insects. They are about 25-50mm in size and they possess clear wings over the abdomen.

Cicadas are said to be periodical if almost all of the cicadas in a given location mature into adults in the same year. The Magicicada septendecim, a most notable periodical cicada, has the longest life cycle of any insect. There are 3 species with 13-year life cycles and another 3 species with 17-year cycles. They are synchronized perfectly that they are nearly absent as adults in the 12 or 16 years between emergence.

Why do these cicadas possess such a long life cycle? What is the significance of having a life cycle being a prime number of years (13 or 17 years)?

Actually, their long life cycles and synchronous emergence help them to escape from natural population control by predators and parasites. If the predator has a life cycle of 2 years, then the cicada has to avoid having a life cycle which is a multiple of 2, otherwise it will be very likely for the cicada to meet its predator. And if the parasite has a life cycle of 5 years, then the cicada has to avoid having a life cycle which is divisible by 5. Consequently, if the cicada has a life cycle being a relatively large prime number (e.g. 13 or 17), then it can avoid coinciding with predators and parasites, since a prime number does not contain any factor except 1 and itself.

For example, if the cicada has a life cycle of 17 years and its parasite has a life cycle of 5 years, then they will only meet every (17x 5) = 85 years, which is the least common multiple of the two numbers. This enables the periodical cicada to escape from the natural population control, and this also accounts for the astounding population density of the cicada – it can get as high as 1.5 million cicadas per acre!

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