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Prime interference

Phys. Rev. Lett. 122, 090201 (2019)

There are many methods for finding prime numbers, some of which date back to antiquity. Timothy Peterson and co-workers have suggested an analogous optical manifestation of the prime number sieve of Eratosthenes by superposing light in multiple diffraction patterns.

The bright spots of a diffraction pattern generated by a grid serve to label a set of discrete points that represent the integer numbers. By superposing Hermite–Gauss beams on this lattice, the amplitude at each point becomes variable and may be zero or finite, depending on the mode selected. Adding multiple grids corresponding to successive prime numbers mimics the iterative elimination of composite numbers suggested by Eratosthenes. Eventually, a finite value in the far-field diffraction pattern indicates a composite number, zero means a prime.

The authors showed simulations for primes up to 31, and suggested that simpler optical sieves could go even further.

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Correspondence to David Abergel.

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Abergel, D. Prime interference. Nat. Phys. 15, 306 (2019).

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