# Understanding Prime Numbers

Prime numbers are positive integers that have fascinated people for thousands of years. If your child struggles to grasp prime numbers, it may help to gain a deeper understanding of how they're defined. Your child may also benefit from knowing how to identify them and how they're useful in nature.

### What Are Prime Numbers?

A prime number is a positive integer that can only be divided without having a remainder by one and itself. Another way of thinking about prime numbers is that they are not the product of two smaller integers. For example, 17, which is a prime number, can't be divided by any number except one and 17, nor is it the product of two smaller numbers. Numbers that aren't prime have more than two divisors. For example, 18 can be divided by one, two, three, six, nine and 18.

Two is the smallest prime number. It's worth noting that one isn't a prime number because it can only be divided by itself and a prime number must have precisely two divisors. There are an infinite number of prime numbers. However, there is no specific formula produces all of the prime numbers.

### Finding Prime Numbers

In Ancient Greece, Eratosthenes developed a 'sieve' that identifies prime numbers. Like a sieve that strains water and leaves pasta behind, the prime number sieve can help your child quickly identify prime numbers. It starts with making a chart that lists every positive integer from one to 100.

First, cross out one, since it isn't prime, and circle two, the smallest prime number. Then cross out every multiple of two. Next, circle three, the next prime number and then cross out every multiple of three that isn't yet crossed out. Continue this process until all numbers from one to 100 have been circled or crossed out. You'll be left with all of the prime numbers between one and 100.

### Prime Numbers and the Evolution of Insects

Prime numbers aren't just an abstract concept; they also appear in nature. Most prominently, the life cycle of cicadas follows a unique prime number-based pattern. The insects live as grubs underground for most of their lives. The only pupate and emerge every 13 or 17 years. When they emerge, they quickly breed and die in a matter of weeks.

It's believed that the emergence pattern of cicadas evolved around prime numbers as a means of survival. If cicadas emerged every 12 or 16 years, for example, then a predator that appears every two years would certainly meet them. The unusual appearance pattern, though, dramatically reduces the likelihood of a predator that's especially adapted to cicadas. A predator would need to mirror the 13 or 17 year pattern exactly, rather than rely on chance. In this way, prime numbers help the cicada species survive.

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