The Prime Number Spiral (a.k.a. the Ulam Spiral) is constructed as follows: Consider a rectangular grid.

We start with the central point and arrange the positive integers in a spiral fashion (anticlockwise).

There is a tendency for the prime numbers to occur on diagonal lines, however far out into the spiral one goes.

It also (a) allows coloring of the prime numbers in various ways, (b) displays a random arrangement to compare with the primes and (c) shows how square and triangular numbers are located on the spiral.