# Uncovering Multiscale Order in the Prime Numbers via Scattering

@article{Torquato2018UncoveringMO, title={Uncovering Multiscale Order in the Prime Numbers via Scattering}, author={Salvatore Torquato and G. Zhang and Matthew de Courcy-Ireland}, journal={arXiv: Statistical Mechanics}, year={2018} }

The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in physics and materials science, we show 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 {\it effectively limit-periodic}. In particular, the primes… Expand

#### 15 Citations

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