  We study implications of the very recently reported mass
$M=2.17^{+0.11}_{-0.10}$M$_\odot$ of PSR~J0740+6620 on the Equation of State
(EOS) of super-dense neutron-rich nuclear matter with respect to existing
constraints on the EOS based on the mass $M=2.01\pm 0.04$M$_\odot$ of
PSR~J0348+0432, the maximum tidal deformability of GW170817 and earlier results
of various terrestrial nuclear laboratory experiments. The lower limit of the
skewness $J_0$ measuring the stiffness of super-dense isospin-symmetric nuclear
matter is raised raised from about -220 MeV to -150 MeV, reducing significantly
its current uncertainty range. The lower bound of the high-density symmetry
energy also increases appreciably leading to a rise of the minimum proton
fraction in neutron stars at $\beta$-equilibrium from about 0 to 5\% around
three times the saturation density of nuclear matter. The difficulties for some
of the most widely used and previously well tested model EOSs to predict
simultaneously both a maximum mass higher than 2.17 M$_\odot$ and a pressure
consistent with that extracted from GW170817 present some interesting new
challenges for nuclear theories.
