Find all the primes between 1 and 15.
These are $2,3,5,7,11,13$. A calculation shows that these numbers are only divisible by 1 and themselves. Conversely, 4 is not prime, because it is divisible by 2 and $2 \neq 1$ and $2 \neq 4$. Similarly, 6 is divisible by 2, 8 is divisible by 2, 9 is divisible by 3, 10 is divisible by 2, 12 is divisible by 2, 14 is divisible by 2 and 15 is divisible by 3.