Prime & Composite Numbers

A prime number has exactly two different factors: $1$ and itself. A composite number has more than two factors.

The primes begin $2, 3, 5, 7, 11, 13, 17, 19, \dots$ Notice that $2$ is the only even prime — every other even number can also be divided by $2$, giving it a third factor.

The number $1$ is special: it has only one factor (itself), so it is neither prime nor composite.

Worked example. Is $15$ prime? Its factors are $1, 3, 5, 15$ — four of them, so $15$ is composite. Is $13$ prime? The only numbers that divide it are $1$ and $13$, so $13$ is prime.