2005 is a composite number (5 x 401).  What is the next year that is a prime number?

 

 

Since every even number (other than 2) is a composite number, we can eliminate each of those.  So the numbers we need to check are odd numbers starting with 2007. 

 

2007 is divisible by 3 since the sum of its digits is divisible by 3 .

 

2009 is not divisible by 2, 3, or 5.  If we try dividing by 7 we find .

 

2011 is not divisible by 2, 3, or 5.  We need to check to see if it is divisible by 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43.  We know we can stop at 43 because .

 

 

Since 2011 is not divisible by any prime number less than its square root, it is prime.