Maybe I'm skimming a little too lightly here, but... diffraction patterns are just a Fourier transform. If you have a look at prime spirals (Ulam spirals and Sacks spirals), it's trivial to see that there is some structure that will turn up in a Fourier transform.
This seems closely related to the work on proving the Riemann hypothesis, where there has been work on attempting to show some quasi-crystalline structure of the zeta function zeros (https://en.wikipedia.org/wiki/Riemann_hypothesis#Quasicrysta...). The Riemann hypothesis itself has deep consequences for the theory of primes. Cool stuff.
> 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. In computer experiments, they bounced light off long prime sequences, such as the million-or-so primes starting from 10,000,000,019.
It sounds like they simulated shining light on particles that were distributed based on the interval between subsequent primes, then looked for patterns in the resulting diffraction. The title was worded that way for a pun (the chemist revealed interesting information about the pattern by literally shining light on it).
"Shining light" on something is kind of a metaphor for figuratively illuminating something, or showing something more clearly (pretend someone shines light on something in the dark). More precisely, I believe this is saying that a chemist is providing more information about a prime number PATTERN.
OK so he takes the Fourier transform of a non-periodic array of delta functions with the delta functions being at the prime positions, and notices peaks at inverse separations of 2, 6, etc. There’s neither X-ray diffraction, chemistry, or any real math here. Garbage.
