Cicadas are a species of bug that when born live in the ground for either 13 or 17 years (depending on the species) While they are underground they survive by eating roots. After 13 or 17 years they emerge from the ground and look for their mates They stay above the ground for 7 days After this they die. We had to pretend that there were 3 predators that were hunting the cicadas: Predator A came out every 2 years, Predator B came out every 3 years and Predator C came out every 4 years. With this information we have to find out what lifecycle (number of years) is the best for the cicadas to live in. In other words weather the cicadas should emerge every 10, 11, 12, 13…or 18 years.

Contents: Table Working Out

=Prime =Composite

We believe that this is not a coincidence, because if you look at our purple table, you can see that when they emerge every prime numbered year (11, 13, 17) have a less likely chance of being eaten -which means a longer life span-, than if they were to emerge in a composite numbered year. Because when there are a lot of divisors there a smaller time span between the years that they could get hunted by predators. Also because the predators come out every 2,3 and 4 years and those are factors of many composite numbers. The cycle lengths that will be at least 100 years before the cicadas are attacked by all three predators are: 11, 13, and 17. We notice that all these numbers are prime.