Searching for a counterexample to Kurepa's Conjecture

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 $!^{k}n=(0!)^k +(1!)^k +\cdots+((n-1)!)^{k}$,andshowthatforallintegers$1<k<100$ there exists an odd prime $p$ such that $p\mid {!}^{k}p$.