  The photon polarization operator in superstrong magnetic fields induces the
dynamical photon "mass" which leads to screening of Coulomb potential at small
distances $z\ll 1/m$, $m$ is the mass of an electron. We demonstrate that this
behaviour is qualitatively different from the case of D=2 QED, where the same
formula for a polarization operator leads to screening at large distances as
well. Because of screening the ground state energy of the hydrogen atom at the
magnetic fields $B \gg m^2/e^3$ has the finite value $E_0 = -me^4/2
\ln^2(1/e^6)$.
