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arXiv · 1409.0800

Searching for a counterexample to Kurepa's Conjecture

Vladica Andrejić·Milos Tatarevic
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Abstract

Kurepa's conjecture states that there is no odd prime $p$ that divides $!p=0!+1!+\cdots+(p-1)!$. We search for a counterexample to this conjecture for all $p<2^{34}$. We introduce new optimization techniques and perform the computation using graphics processing units. Additionally, we consider the generalized Kurepa's left factorial given by $!^{k}n=(0!)^k +(1!)^k +\cdots+((n-1)!)^{k}$, and show that for all integers $1<k<100$ there exists an odd prime $p$ such that $p\mid !^k p$.

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Vladica Andrejić, Milos Tatarevic. 2014-09-02. Searching for a counterexample to Kurepa's Conjecture. https://doi.org/10.1090/mcom/3098

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