CICADAS KNOW THEIR PRIME NUMBERS

Cicadas are large insects that appear periodically in massive numbers. They are known as a symbol of resurrection because of their interesting life cycle, based on prime numbers.

Cicada in Princeton, NJ

Although Cicadas spend most of their life underground, they eventually have to come up to the surface for sunlight and reproduction. While on the ground, these insects mate and lay their eggs on tree branches. These eggs then take about 6-7 weeks to hatch, after which they burrow into the soil and continue this life cycle.

However, when Cicadas do emerge at the surface, there are many dangers awaiting. These insects are easily eaten by birds, bats, spiders, wasps, and the list goes on and on.

You may be wondering how this species has not gone extinct yet, as it has so many predators. This is where the prime numbers come into play.

Cicadas that leave their underground habitat within a year or two are quickly devoured by scavenging predators. However, this doesn’t mean that the longer they remain underground, the longer they survive. Some Cicadas that don’t come up to the surface for 15 years or 18 years still get eaten faster than those that emerge in 13 years or 17 years. How is this possible?

Periodical cicadas have the longest life cycle, coming up every 13 or 17

years, longer than an annual cicada in comparison. Due to these specific prime number life cycles, predators find it very difficult to catch these types of periodical cicadas.

Prime Numbers:

Prime numbers are whole numbers greater than 1 that cannot be divided exactly by any positive integer other than itself and 1.

Every single number can be written as the product of prime numbers and every integer larger than 2 can be written as the sum of two prime numbers.

How do these prime number properties relate to the cicadas’ life cycle though?

Cicadas are not the only living species with their own unique life cycle. Their predators also have one, which can be 3, 4, 5, 6, or any number of years long. Take the wasp for example, which has a life cycle of 4 years. This means that every 4th, 8th, 12th, and so on year, the cicadas will be open to being eaten by the wasps.

What if the cicadas had a life cycle of 8 years? They will be vulnerable to any predators blossoming on a 1, 2, 4, or 8 year cycle.

Since their predators have shorter life cycles, they prey on cicadas the year that is a multiple of the # of years in their life cycle. So with prime #s, there are fewer chances of the predator life cycle to align with the cicadas cycle.

Cicadas with a 12 year life cycle have the least chance of surviving the longest because of 12 has many factors, 1, 2, 3, 4, 5, 6, 12. Predators with any of these life cycles can catch cicadas. If the predator has a 2 year cycle, they will catch them every 6th year since 2 x 6 = 12. If the predator has a 3 year cycle, they will catch them every 4th year since 3 x 4 = 12. This pattern repeats for all of the factors.

Using this strategy, cicadas have evolved to emerge every 13th or 17th year. There are many predators with life cycles between 2-12 years without a factor aligning with 13 or 17. For example if the predator has a 7 year cycle, they have a smaller chance of catching the 17-year cycling Cicadas since 7 x 2 = 14 and 7 x 3 = 21, skipping over 17. Using this method, the same result can be found for 13-year cycling Cicadas.

Why don’t Cicadas survive as much in other prime number years? The reason for this is that if these insects emerge before 13 years, like in 11 years, then starving predators awaiting their arrival quickly finish them. If they wait for more than 17 years, like 19 years, then predators would have finished and digested their last meal, ready to eat the next round of Cicadas.

Let’s use a predator with a 6 year life cycle as an example.

With a 13-year cycling Cicada, the probability of the insect getting caught is 6 x 13 = 78 years, while with a 17-year cycling Cicada, the chance would be 6 x 17 = 102 years. This is a much longer span than if the life cycle was not following this prime number method.

Another way these prime numbers 13 and 17 prove to be useful includes the rare chance of any of these periodically rotating species to interbreed with non prime number cycling breeds.

For example, cicadas breeds with life cycles 8 and 10 have a much larger chance of interbreeding and mixing species. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80. Multiples of 10 include 10, 20, 30, 40, 50, 60, 70, and 80. This means these two breeds of Cicadas will interact and emerge on the ground level together every 40 years, which is often.

On the other hand, breeds of this insect with cycles of 13 and 17 interact much less often. Being prime numbers, they don’t have any common multiples until their product, 221.

This means that these two breeds of Cicadas won’t interact for 221 years. The last time both of these breeds interacted amongst each other was in the year 2015, which makes the next time they emerge together the year 2236, 221 years from 2015.

Clearly, prime numbers play a huge role in the evolution of Cicadas. Math is useful not only for our species, but even in nature for insects as small as Cicadas.