7 research outputs found
On Limits of Dense Packing of Equal Spheres in a Cube
We examine packing of congruent spheres in a cube when is close but
less than the number of spheres in a regular cubic close-packed (ccp)
arrangement of spheres. For this family of packings, the
previous best-known arrangements were usually derived from a ccp by omission of
a certain number of spheres without changing the initial structure. In this
paper, we show that better arrangements exist for all . We introduce an optimization method to reveal improvements of
these packings, and present many new improvements for
Improved algorithms for left factorial residues
We present improved algorithms for computing the left factorial residues . We use these algorithms for the calculation of the residues , for all primes up to . Our results confirm that Kurepa's left factorial conjecture is still an open problem, as they show that there are no odd primes such that divides . Additionally, we confirm that there are no socialist primes with
Improved algorithms for left factorial residues
Article 106078International audienceWe present improved algorithms for computing the left factorial residues . We use these algorithms for the calculation of the residues , for all primes up to . Our results confirm that Kurepa's left factorial conjecture is still an open problem, as they show that there are no odd primes such that divides . Additionally, we confirm that there are no socialist primes with