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
