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.
- 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).
- S. Torquato1, G. Zhang, and M. de Courcy-Ireland, Hidden Multiscale Order in the Primes, Journal of Physics A: Mathematical and Theoretical, 52 135002 (2019).