A Chemist Shines Light on a Surprising Prime Number Pattern

Natalie Wolchover in Quanta:

About a year ago, the theoretical chemist Salvatore Torquato met with the number theorist Matthew de Courcy-Ireland to explain that he had done something highly unorthodox with prime numbers, those positive integers that are divisible only by 1 and themselves.

A professor of chemistry at Princeton University, Torquato normally studies patterns in the structure of physical systems, such as the arrangement of particles in crystals, colloids and even, in one of his better-known results, a pack of M&Ms. In his field, a standard way to deduce structure is to diffract X-rays off things. When hit with X-rays, disorderly molecules in liquids or glass scatter them every which way, creating no discernible pattern. But the symmetrically arranged atoms in a crystal reflect light waves in sync, producing periodic bright spots where reflected waves constructively interfere. The spacing of these bright spots, known as “Bragg peaks” after the father-and-son crystallographers who pioneered diffraction in the 1910s, reveals the organization of the scattering objects.

Torquato told de Courcy-Ireland, a final-year graduate student at Princeton who had been recommended by another mathematician, that a year before, on a hunch, he had performed diffraction on sequences of prime numbers. Hoping to highlight the elusive order in the distribution of the primes, he and his student Ge Zhang had modeled them as a one-dimensional sequence of particles — essentially, little spheres that can scatter light.

More here.