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