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). The prime numbers are then marked. There is a tendency for the prime numbers to occur on diagonal lines, however far out into the spiral one goes. This is software is for exploring the Prime Number Spiral. 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.