Explanation:

A natural number is called a prime number (or a prime) if it is bigger than one and has no divisors other than 1 and itself. (Our solved example in mathguru.com uses this concept)

For example, 5 is prime, since no number except 1 and 5 divides it. On the other hand, 6 is not a prime (it is composite), since 6 = 2 · 3.

http://en.wikipedia.org/wiki/Prime_number

A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number. (Our solved example in mathguru.com uses this concept)

By definition, every integer greater than one is either a prime number or a composite number. The number one is a unit - it is neither prime nor composite. For example, the integer 14 is a composite number because it can be factored as 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself.

The first 105 composite numbers are

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, (Our solved example in mathguru.com uses this concept) 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140.

http://en.wikipedia.org/wiki/Composite_number

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.