We present improved algorithms for computing the left factorial residues !p=0!+1!+…+(p−1)!modp. We use these algorithms for the calculation of the residues !pmodp, for all primes p up to 240. Our results confirm that Kurepa's left factorial conjecture is still an open problem, as they show that there are no odd primes p<240 such that p divides !p. Additionally, we confirm that there are no socialist primes p with 5<p<240.