  The recent high-precision data for the reaction $\gamma p\to p\eta'$ at
photon energies in the range 1.5--2.3 GeV obtained by the CLAS collaboration at
the Jefferson Laboratory have been analyzed within an extended version of the
photoproduction model developed previously by the authors based on a
relativistic meson-exchange model of hadronic interactions [Phys. Rev. C
\textbf{69}, 065212 (2004)]. The $\eta'$ photoproduction can be described quite
well over the entire energy range of available data by considering $S_{11}$,
$P_{11}$, $P_{13}$, and $D_{13}$ resonances, in addition to the $t$-channel
mesonic currents. The observed angular distribution is due to the interference
between the $t$-channel and the nucleon $s$- and $u$-channel resonance
contributions. The $j=3/2$ resonances are required to reproduce some of the
details of the measured angular distribution. For the resonances considered,
our analysis yields mass values compatible with those advocated by the Particle
Data Group. We emphasize, however, that cross-section data alone are unable to
pin down the resonance parameters and it is shown that the beam and/or target
asymmetries impose more stringent constraints on these parameter values. It is
found that the nucleonic current is relatively small and that the
$NN\eta^\prime$ coupling constant is not expected to be much larger than 2.
