Searching for a counterexample to Kurepa's conjecture

Abstract

Kurepa's conjecture states that there is no odd prime p that divides !p=0!+1!+..+(p-1)!. We search for a counterexample to this conjecture for all p < 234. We introduce new optimization techniques and perform the computation using graphics processing units. Additionally, we consider the generalized Kurepa's left factorial given by !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.