Divisibility and primes

What properties can integers ( 0, 1, 2, ….) have?

One property is divisibility: We say that integer a divides integer b, notation a∣b, if there is an integer c so that a*c=b. If such an integer does not exist a∤b.

We can plot b horizontally and a vertically we can put a∎ in when a∣b:

9 | ∎ | ||||||||

8 | ∎ | ||||||||

7 | ∎ | ||||||||

6 | ∎ | ||||||||

5 | ∎ | ||||||||

4 | ∎ | ∎ | |||||||

3 | ∎ | ∎ | ∎ | ||||||

2 | ∎ | ∎ | ∎ | ∎ | |||||

1 | ∎ | ∎ | ∎ | ∎ | ∎ | ∎ | ∎ | ∎ | ∎ |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

This starts showing some patterns: the lines like the diagonal originating

On this page I show a plot on 'millimeter paper' of numbers and their divisors.

X and Y pairs are like:

The X axis shows an integer, and the Y axis too. The square is black when y divides x. This shows both patterns and a kind of chaos: for me it is like a bubble chamber revealing the tracks of subatomic particles and cosmic mysteries. There is a beautifull site devoted to these patterns: divisorplot.com.

This version allows you to travel alang the number line at varying speed (the graphics are not yet optimal) clicking < or > you can increase or decrease speed. Watch the stroboscopic effects!

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