To perform the Sieve of Eratosthenes, start by clicking on 2. This will "take out" all of the even numbers. The next number with a white background will be 3 -- the next prime. Click on the 3, and you will take out all of the numbers divisible by 3.
Continue like this, clicking on 5, 7, 11, and so on. As you continue, the next number with a white background will always be the next prime.
As you do this, look at the patterns, or lines, that get colored in each time you click. You can think of the sieve as weaving together these threads, and the primes are just the holes in the cloth. As we get to larger numbers we have more threads and fewer holes: there aren't as many prime numbers. Can you use this intuition to guess how many prime numbers there will be between one billion and 2 billion? How about 1 googol and 2 googol?
Use the controls at the top of the table to change the size of the grid, change the color schemes, and more. Get in and explore!
See the wikipedia article to learn more.