  The quantum kicked prime number rotator (QKPR) is defined as the rotator
whose energy levels are prime numbers. The long time behavior is decided by the
kick period $\tau$ and kick strength $k$. When $\frac{\tau}{2\pi}$ is
irrational, QKPR is localized because of the equidistribution theorem. When
$\frac{\tau}{2\pi}$ is rational, QKPR is localized for small $k$, because the
system seems like a generalized kicked dimer model. We argue for rational
$\frac{\tau}{2\pi}$ QKPR delocalizes for large k.
