2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141128The 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 $τ$ and kick strength $k$. When $\fracτ{2π}$ is irrational, QKPR is localized because of the equidistribution theorem. When $\fracτ{2π}$ is rational, QKPR is localized for small $k$, because the system seems like a generalized kicked dimer model. We argue for rational $\fracτ{2π}$ QKPR delocalizes for large k.6 pages, 6 figuresChaotic Dynamicstext