  Using $1.09\times10^{9}$ $J/\psi$ events collected by the BESIII experiment
in 2012, we study the $J/\psi\rightarrow\gamma\eta^{\prime}\pi^{+}\pi^{-}$
process and observe a significant abrupt change in the slope of the
$\eta^{\prime}\pi^{+}\pi^{-}$ invariant mass distribution at the
proton-antiproton ($p\bar{p}$) mass threshold. We use two models to
characterize the $\eta^{\prime}\pi^{+}\pi^{-}$ line shape around
$1.85~\text{GeV}/c^{2}$: one which explicitly incorporates the opening of a
decay threshold in the mass spectrum (Flatt\'{e} formula), and another which is
the coherent sum of two resonant amplitudes. Both fits show almost equally good
agreement with data, and suggest the existence of either a broad state around
$1.85~\text{GeV}/c^{2}$ with strong couplings to $p\bar{p}$ final states or a
narrow state just below the $p\bar{p}$ mass threshold. Although we cannot
distinguish between the fits, either one supports the existence of a $p\bar{p}$
molecule-like state or bound state with greater than $7\sigma$ significance.
