  A short review of Schroedinger hamiltonians for which the spectral problem
has been related in the literature to the distribution of the prime numbers is
presented here. We notice a possible connection between prime numbers and
centrifugal inversions in black holes and suggest that this remarkable link
could be directly studied within trapped Bose-Einstein condensates. In
addition, when referring to the factorizing operators of Pitkanen and Castro
and collaborators, we perform a mathematical extension allowing a more standard
supersymmetric approach
