  We present improved algorithms for computing the left factorial residues
$!p=0!+1!+...+(p-1)! \!\mod p$. We use these algorithms for the calculation of
the residues $!p\!\mod p$, for all primes $p$ up to $2^{40}$. Our results
confirm that Kurepa's left factorial conjecture is still an open problem, as
they show that there are no odd primes $p<2^{40}$ such that $p$ divides $!p$.
Additionally, we confirm that there are no socialist primes $p$ with
$5<p<2^{40}$.
