Cicadas & Prime Numbers

Cicadas & Prime Numbers

Part of the survival strategy of cicadas is to emerge in prime number intervals.

There are thousands of species of cicadas. As nymphs they live most of their lives underground, only to emerge when they are ready to transform into adults, sing, mate, and die. Their time above ground is about a month.

Broadly speaking cicadas can be divided into two groups:
• Annual cicadas: those with relatively short life cycles, some of which appear every year
• Periodical cicadas: those that live underground for over a decade and only come above ground in synchronized intervals

Periodical cicadas are found only in the eastern areas of North America. Instead of a few here and a few there coming above ground every year, periodical cicadas (divided up into 15 geographic broods) appear all together at designated intervals. Their synchronized appearances, every 13 years or every 17 years, is what makes them remarkable.

Prime Number Survival

Part of the survival strategy of the periodical cicadas is that they appear all together. Millions to billions of cicadas all emerging in the same short window of time ensures that, while many will be killed by predators, the majority will survive to continue the species. Simply put, there are so many cicadas appearing all at once that predators can’t eat them fast enough – a survival concept known as predator satiation.

Predator satiation is a numbers game. It only works in large numbers relative to the number of predators. For a brood of periodical cicadas this means they have to be synchronized and appear all at the same time otherwise their numbers might be too low, too many may be eaten, and they could die off.

What a brood of periodical cicadas doesn’t want is another brood appearing at the same time. For one thing they would be competing for resources. What’s worse is if a 13 year brood and a 17 year brood interbreed then the inner clocks of their offspring may become confused. The result could ruin the synchronized timing of their appearances which they need for predator satiation. Their survival depends on avoiding other broods of cicadas. Enter, prime numbers.

Taking into consideration reasonable lifespans for cicadas, composite number intervals would have broods appearing in the same year more frequently than the prime number intervals of every 13 or 17 years.

Prime numbers are numbers only divisible by themselves and 1. The periodical cicadas of North America appear in prime number intervals of either 13 or 17 years. If you create a list of years, and mark every 13 years as well as every 17 years, they rarely overlap. In fact, 13 year cicadas and 17 year cicadas only overlap every 221 years. If they appeared in composite number intervals, (4, 6, 8, 9, etc) they would overlap constantly and most likely die out. Through evolution, the periodical cicadas that used prime numbers have survived.

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