The Ulam Spiral

In 1963, mathematician Stanisław Ulam was bored during a long meeting. He arranged the integers in a spiral on graph paper and noticed primes clustering on diagonals. No one had predicted this.

The diagonals correspond to quadratic polynomials that generate unusually many primes. The most famous, n² + n + 41, produces primes for n = 0 through 39. Why primes cluster along these lines remains partially unsolved.