The prime numbers have been a source of fascination for millennia and

continue to surprise us. Motivated by the hyperuniformity concept, we have

shown that the prime numbers in certain large intervals possess

unanticipated order across length scales and represent the first example

of a new class of many-particle systems with pure point diffraction

patterns, which we call *effectively limit-periodic*.

**References**

- G. Zhang, F. Martelli and S. Torquato, The Structure Factor of Primes,
**Journal of Physics A: Mathematical and Theoretical**,**51**, 115001 (2018). - S. Torquato, G. Zhang, and M. de Courcy-Ireland, Uncovering Multiscale Order in the Prime Numbers via Scattering,
**Journal of Statistical Mechanics: Theory and Experiment**,**2018**093401 (2018).