Say for example you have the number 139. If it is not prime it's divisible by some number less than . So start making a list:

.

.

.

139 is not divisible by any of the numbers 2, 3, ..., 12. Thus 139 is prime. (Actually you don't need to divide by all of 2, 3, ..., 12, you may simply divide by all primes less than 12: 2, 3, 5, 7, and 11.)

Try 527. We need to check divisibility by all numbers less than .

.

.

.

Thus and thus it is not a prime number.

-Dan