Prime Time 

What are prime numbers?

A prime number is a positive integer that can only be divided evenly by by 2 different integers 1 and itself.  5 can only be divided evenly by 5 and 1 so this number is prime.  6 can be divided evenly by 2, 3, 6, and 1 so 6 would not be a prime number.

Some fun facts:

• 1 is not a prime number.  It is defined as not prime and is not divisible by 2 different integers.  It is only divisible by 1.
• 2 is the only even prime number.
• Numbers that are greater than one and not prime are called composite numbers.
• There are infinitely many prime numbers.
• 0 is not a prime number.

How do we determine if a number is prime?

You can easily figure out if a number is prime by dividing by smaller prime numbers to see if it can be evenly divided.  If I want to find out if 11 prime, I can try to divide it by smaller prime numbers like 2,3,5, or 7.  11 cannot be evenly divided by any smaller prime factors therefore it is prime.  If I wanted to find out if 33 is prime, I can divide 33 by 3 and I find it will evenly divide into 33 with factors of 1,3,11, and 33, therefore it is not prime.

Following are the prime numbers less than 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Practice:

Find out if the following numbers are prime:  101, 123 149, and 171.

Definitions:

Divide evenly:  To divide evenly means that if you divide one number by another there is no remainder.  We can make this easier by saying that it will not produce a non integer.  4 divided by 3 = 1.33333..... which is not an integer so 4 is not evenly divisible by 3.