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!