Observation of $\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{0}\pi^{0}$

Using a sample of $1.3\times 10^9$ $J/\psi$ events collected with the BESIII detector, we report the first observation of $\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{0}\pi^{0}$. The measured branching fractions are $\mathcal{B}$($\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{+}\pi^{-}$) = $(8.53\pm0.69({\rm stat.})\pm0.64({\rm syst.}))\times10^{-5}$ and $\mathcal{B}$($\eta^{\prime}\to\pi^{+}\pi^{-}\pi^{0}\pi^{0}$) = $(1.82\pm0.35({\rm stat.})\pm0.18({\rm syst.}))\times10^{-4}$, which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.