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Journal Articles Information Processing Letters Year : 2021

Improved algorithms for left factorial residues

Abstract

We present improved algorithms for computing the left factorial residues $!p=0!+1!+\dots+(p-1)! \!\mod p$. We use these algorithms for the calculation of the residues $!p\!\mod p$, for all primes $p$ up to $2^{40}$. Our results confirm that Kurepa's left factorial conjecture is still an open problem, as they show that there are no odd primes $p<2^{40}$ such that $p$ divides $!p$. Additionally, we confirm that there are no socialist primes $p$ with $5
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Dates and versions

hal-02411741 , version 1 (03-02-2023)

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Vladica Andrejić, Alin Bostan, Milos Tatarevic. Improved algorithms for left factorial residues. Information Processing Letters, 2021, 167, pp.3. ⟨10.1016/j.ipl.2020.106078⟩. ⟨hal-02411741⟩
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