composite number

A composite number is a positive integer which is not prime and not equal to 1. That is, $n$ is composite if $n = ab$ , with $a$ and $b$ natural numbers both not equal to 1.

Examples.

• 1 is not composite (and also not prime), by definition.
• 2 is not composite, as it is prime.
• 15 is composite, since $15 = 3\cdot 5$ .
• 93555 is composite, since $93555 = 3^5\cdot 5 \cdot 7 \cdot 11$ .
• 52223 is not composite, since it is prime.

More generally, we can define compositeness any time there is an ambient notion of an irreducible element. In an integral domain, for example, an element is said to be composite if it neither zero, a unit, nor irreducible.