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arXiv · 1904.09196

Improved algorithms for left factorial residues

Vladica Andrejić·Alin Bostan·Milos Tatarevic
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Abstract

We present improved algorithms for computing the left factorial residues $!p=0!+1!+...+(p-1)! \!\mod p$. 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 $5<p<2^{40}$.

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Vladica Andrejić, Alin Bostan, Milos Tatarevic. 2019-04-19. Improved algorithms for left factorial residues. https://arxiv.org/abs/1904.09196

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