high performance computing on graphics processing units: hgpu.org

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.