Section: New Results

Improved algorithms for left factorial residues

In [11], Alin Bostan together with Vladica Andrejić (University of Belgrade, Serbia) and Milos Tatarevic (CoinList, Alameda, CA) presented improved algorithms for computing the left factorial residues $!p=0!+1!+\cdots +(p-1)!modp$. They used these algorithms for the calculation of the residues $!pmodp$, for all primes $p$ up to $2^{40}$. Their 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, they confirmed that there are no socialist primes $p$ with $5<p<2^{40}$.