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A '''prime number''' is a number that is evenly divisible by no other number except for itself and 1.  A number which is not prime is called a [[composite number]].  The classifications ''prime'' and ''composite'' apply to positive integers greater than 1, though there are related concepts in other branches of mathematics.  Note that 1 is neither prime nor composite.

A '''prime number''' is a number that is evenly divisible by no other number except for itself and 1.  A number which is not prime is called a [[composite number]].  The classifications ''prime'' and ''composite'' apply to positive integers greater than 1, though there are related concepts in other fields of mathematics.  Note that 1 is neither prime nor composite.

The smallest prime numbers are 2, 3, 5, 7, 11, 13... .  An exmple of a composite number is 6, which is easily divisible by both 2 and 3.

The smallest prime numbers are 2, 3, 5, 7, 11, 13... .  An exmple of a composite number is 6, which is evenly divisible by both 2 and 3.

 

It is easy to prove that there are an infinite number of primes.  If there were a finite number of primes, you could multiply them all together and add 1.  The resulting number would have to be a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).