  The neutron skin thickness $\Delta r_{\rm{np}}$ of heavy nuclei is
essentially determined by the symmetry energy density slope $L({\rho })$ at
$\rho_c = 0.11/0.16\rho_0$ ($\rho_0$ is nuclear saturation density), roughly
corresponding to the average density of finite nuclei. The PREX collaboration
recently reported a model-independent extraction of $\Delta r^{208}_{\rm{np}} =
0.29 \pm 0.07$ fm for the $\Delta r_{\rm{np}}$ of $^{208}$Pb, which suggests a
rather stiff symmetry energy $E_{\rm{sym}}({\rho })$ with $L({\rho_c }) \ge 55$
MeV. We demonstrate that the $E_{\rm{sym}}({\rho })$ cannot be too stiff and
$L({\rho_c }) \le 73$ MeV is necessary to be compatible with (1) the
ground-state properties and giant monopole resonances of finite nuclei, (2) the
constraints on the equation of state of symmetric nuclear matter at
suprasaturation densities from flow data in heavy-ion collisions, (3) the
largest neutron star (NS) mass reported so far for PSR J0740+6620, (4) the NS
tidal deformability extracted from gravitational wave signal GW170817 and (5)
the mass-radius of PSR J0030+045 measured simultaneously by NICER. This allow
us to obtain $55 \le L({\rho_c }) \le 73$ MeV and $0.22 \le \Delta
r^{208}_{\rm{np}} \le 0.27$ fm, and further $E_{\rm{sym}}({\rho_0 }) = 34.5 \pm
1.5$ MeV, $L({\rho_0 }) = 85.5 \pm 22.2$ MeV, and $E_{\rm{sym}}({2\rho_0 }) =
63.9 \pm 14.8$ MeV. A number of critical implications on nuclear physics and
astrophysics are discussed.
