In spring several years ago, cicadas were forecast to come to the eastern United States. How could they have predicted the appearance of a particular herd of cicadas like the weather forecast, even though there is no observation device for it? It is possible because they are the 17-year cicadas that appear explosively in a certain area every 17 years.
Mathematical secrets are hidden in the lifespan of cicadas. Cicadas’ life expectancy is a prime number such as 5 years, 7 years, 11 years, 13 years, and 17 years, including the period of time living as nymph under the ground, depending on the species. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. And a composite number is a positive integer that can be formed by multiplying together two smaller positive integers; for example, 4, 6, 8, 9, 10, and 12. If the lifespan of the cicadas is a composite number, there is a higher risk of meeting their natural enemies in the same year and of decreasing their population. What is worse, cicadas with a different life expectancy may appear in the same year, and competing for food will become intense. The reason cicadas’ lifespan is a prime number is closely related to their survival.
Until they develop from nymphs into imagos, they live underground for a long time. When cicadas come out to the world, they live only 7 to 20 days. The invisible hand that enables them to avoid risk factors as much as possible for their short life is marvelous.