The prime number spiral, also known as the Ulam spiral, is a graphical representation in which positive integers are arranged in a spiral shape, with prime numbers being somehow indicated along this spiral.

It was discovered by mathematician Stanislaw Ulam in 1963 while scribbling on paper because he was bored during a scientific meeting. He found that the numbers indicated tended to cluster according to diagonals. According to the image below, where the prime numbers are marked in black, the diagonals are perfectly visible, confirming the pattern, which remains to be explained.