  We report the first experimental realization of the prime number quantum
potential $V_N(x)$, defined as the potential entering the single-particle
Schr\"{o}dinger Hamiltonian with eigenvalues given by the first $N$ prime
numbers. We use holographic optical traps and, in particular, a spatial light
modulator to tailor the potential to the desired shape. As a further
application, we also implement a potential with lucky numbers, a sequence of
integers generated by a different sieve than the familiar Eratosthenes's sieve
used for the primes.
  Our results pave the way towards the realization of quantum potentials with
arbitrary sequences of integers as energy levels and show, in perspective, the
possibility to set up quantum systems for arithmetic manipulations or
mathematical tests involving prime numbers.
