A visualization of the Sieve of Eratosthenes Each number on the x axis shows its largest prime factor in the y axis. When the largest prime factor is itself, the number is prime and the bar is highlighted in blue. You can see multiples of prime numbers if you scan at any particular height from left to right. The usual 2D arrangement is necessary on paper or a non-interactive medium, but if you have a touch screen with pan and pinch zoom it seems nicer to spread the numbers out in a single line. There's an overlay always visible to show you which number each bar is for. Where the bar occludes the overlay it's easy to deduce from neighboring numbers on the overlay. Each composite mentions its largest prime factor, so you can see at a glance why it's composite. And scanning to the left also gives you a visual "proof" of compositeness; you can see the grey bars of that height stretching leftward at a regular cadence.