  We report the first experimental demonstration of prime number sieve via
linear optics. The prime numbers distribution is encoded in the intensity zeros
of the far field produced by a spatial light modulator hologram, which
comprises a set of diffraction gratings whose periods correspond to all prime
numbers below 149. To overcome the limited far field illumination window and
the discretization error introduced by the SLM finite spatial resolution, we
rely on additional diffraction gratings and sequential recordings of the far
field. This strategy allows us to optically sieve all prime numbers below
$149^2=22201$.
