We construct an analog computer based on light interference to encode the hyperbolic function f({zeta}) = 1/{zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number
decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j>2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a single run w
ithout precalculating the ratio N/l, where l are all the possible trial factors. Continuous truncated exponential sums turn out to be a powerful tool for distinguishing factors from non-factors (we also suggest, with regard to this topic, to read an interesting paper by S. Woelk et al. also published in this issue [Woelk, Feiler, Schleich, J. Mod. Opt. in press]) and factorizing different numbers at the same time. We will also describe two possible M-path optical interferometers, which can be used to experimentally realize this algorithm: a liquid crystal grating and a generalized symmetric Michelson interferometer.
