The discovery may aid research in both mathematics and materials science. "Prime numbers have beautiful structural properties, including unexpected order, hyperuniformity and effective limit-periodic behavior," said Torquato. "The primes teach us about a completely new state of matter."

"What's fascinating about this paper is that it gives us a different perspective on the primes: instead of viewing them as numbers, we can view them as particles and try to map out their structure via X-ray diffraction," said Henry Cohn, a principal researcher at Microsoft Research who was not involved with the study. "It turns out to give us the same sort of information as traditional number-theoretic methods, and to tie in beautifully with previous work. It's a beautiful new perspective on this information, and it opens up new connections with materials science and scattering theory."