  We prove a rigorous lower bound on the correlation energy of interacting
fermions in the mean-field regime for a wide class of singular interactions,
including the Coulomb potential. Combined with the upper bound obtained in
\cite{ChrHaiNam-23b}, our result establishes an analogue of the
Gell-Mann--Brueckner formula $c_{1}\rho\log\left(\rho\right)+c_{2}\rho$ for the
correlation energy of the electron gas in the high-density limit. Moreover, our
analysis allows us to go beyond mean-field scaling while still covering the
same class of potentials.
