Improved algorithms for left factorial residues

04/19/2019

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by   Vladica Andrejić, et al.

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We present improved algorithms for computing the left factorial residues !p=0!+1!+...+(p-1)! p. We use these algorithms for the calculation of the residues !p 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.