# Prime Number

Pronunciation: /praɪm ˈnʌm.bər/ Explain

A prime number is an integer that is evenly divisible only by 1 and itself. An example of a prime number is the integer 5. The only integers that divide evenly into 5 are 1 and 5. If we try to divide 5 by 2, we get 2 1/2, which is not an integer.

A composite number is an integer that is not prime. 6 is not a prime number. 6 is evenly divisible by both 2 and 3, so 6 is a composite number.

### How to Tell if a Number is Prime

A prime number is an integer that is divisible only by one and itself. If one tests all prime numbers starting with 2 up to the square root of a number, and none of them divides the number evenly, the number is a prime number.

The reason one only needs to test prime numbers, is that if a number is not prime, it has smaller factors which have already been tested. Take 6, for example. 6 = 2 · 3. Since one starts with 2, 2 and 3 have already been tested. If neither divides the number evenly, then 6 = 2 · 3 will also not divide the number evenly.

Testing 11 to See if it is Prime
StepEquation(s)Description
1 Get the square root of the number. We will be testing all prime numbers less than the square root. Since the square root of 11 is about 3.3166, we will be testing all prime numbers less than 3.3166.
2 11 ÷ 2 = 5.5 Test by dividing 11 by 2. Since 11 ÷ 2 = 5.5, and 5.5 is not an integer, 11 is not divisible by 2.
3 11 ÷ 3 ≈ 3.6666 Test by dividing by 3. The quotient is not an integer, so 11 is not divisible by 3.
4 5 > 3.3166 The next prime number is 5. Since 5 is greater than 3.3166, we are done. Since no prime number less than the square root of 11 divides 11 evenly, 11 is prime.

1. McAdams, David E.. All Math Words Dictionary, prime number. 2nd Classroom edition 20150108-4799968. pg 144. Life is a Story Problem LLC. January 8, 2015. Buy the book

• Malkevitch, Joseph. Primes. ams.org. American Mathematical Society. 2/6/2010. http://www.ams.org/featurecolumn/archive/primes1.html.

McAdams, David E. Prime Number. 4/28/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/p/primenumber.html.

### Revision History

4/28/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)