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We advance a general theory of field correlation revivals of structuredrandom wave packets, composed of superpositions of propagation-invariant modes,at pairs of planes transverse to the packet propagation direction. We derive anelegant analytical relation between the normalized intensity autocorrelationfunction of thus structured paraxial light fields at a pair of points on anoptical axis of the system and a Gauss sum, thereby establishing a fundamentallink between statistical optics and number theory. We propose andexperimentally implement a simple, robust analog random wave computer that canefficiently decompose numbers into prime factors.

Axial correlation revivals and number factorization with structured random waves