Sieve of Eratosthenes
The Sieve of Eratosthenes is a simple method to quickly uncover a short list of primes. Begin by writing positive numbers starting with 
up to the maximal number you are interested in. Now, during each step, take the first number that is neither crossed, nor circled, circle it, and cross all larger numbers divisible by it. Keep doing this until all numbers are either circled or crossed. The circled numbers are the primes!
Example
It would be nice to really run the sieve up to 15 or 20; unfortunately, I could not find any good way to represent circled and crossed out numbers; italic and bold styles are not distinctive enough and to create crossed numbers in LaTeX is a headache. Maybe somebody else has an idea how to do it...
