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Finding the factors of an integer can be achieved by various experimentaltechniques, based on an algorithm developed by Schleich et al., which usesspecific properties of Gau\ss{}sums. Experimental limitations usually requiretruncation of these series, but if the truncation parameter is too small, it isno longer possible to distinguish between factors and so-called "ghost"factors. Here, we discuss two techniques for distinguishing between truefactors and ghost factors while keeping the number of terms in the sum constantor only slowly increasing. We experimentally test these modified algorithms ina nuclear spin system, using NMR.

NMR implementation of Factoring Large Numbers with Gau\ss{}Sums: Suppression of Ghost Factors