# Laboratoire Collisions Agrégats Réactivité - UMR5589

Université Paul Sabatier - Bat. 3R1b4 - 118 route de Narbonne 31062 Toulouse Cedex 09, France

## Factoring numbers with interfering random waves

We report on a new implementation of the factorisation of numbers using Gauss sums which improves tremendously the efficiency to eliminate all "ghost" factors. We show that by choosing randomly the terms in the Gauss sum, the required number of terms varies as lnN instead of \sqrt[4]N . As an illustration, we present experimental results obtained by interfering thirty ultrashort laser pulses where we factorise 1340333404807. This new approach is totally general and can be implemented for all the experiments based on the Gauss sum.

doi : 10.1209/0295-5075/83/34008

Voir en ligne : EPL, 83, 34008 (2008)