## Searching for a counterexample of Kurepa’s Conjecture

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

arXiv:1409.0800 [math.NT], (2 Sep 2014)

@article{2014arXiv1409.0800A,

author={Andreji{‘c}}, V. and {Tatarevic}, M.},

title={"{Searching for a counterexample of Kurepa’s Conjecture}"},

journal={ArXiv e-prints},

archivePrefix={"arXiv"},

eprint={1409.0800},

primaryClass={"math.NT"},

keywords={Mathematics – Number Theory, 11B83},

year={2014},

month={sep},

adsurl={http://adsabs.harvard.edu/abs/2014arXiv1409.0800A},

adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

Kurepa’s conjecture states that there is no odd prime p which divides !p=0!+1!+…+(p-1)!. We search for a counterexample of this conjecture for all p<10^10. We introduce new optimization techniques and perform the computation using graphics processing units (GPUs). Additionally, we consider the generalized Kurepa’s left factorial given as !kn=(0!)k+(1!)k+…+((n-1)!)k and show that for all integers 1<k<100 there exists an odd prime p such that p|!^kp.

September 3, 2014 by hgpu