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## Section: New Results

### Fast arithmetic for faster integer multiplication

Participants : Svyatoslav Covanov [contact] , Emmanuel Thomé.

The paper [20] describes an algorithm for the multiplication of two $n$-bit integers. It achieves the best asymptotic complexity bound $O\left(nlogn·{4}^{{log}^{*}n}\right)$ under a hypothesis on the distribution of generalized Fermat primes of the form ${r}^{{2}^{\lambda }}+1$. This hypothesis states that there always exists a sufficiently small interval in which we can find such a prime. Experimental results give evidence in favor of this assumption. A journal submission is planned shortly.