  We perform systematic calculations of pairing gaps in semi-magic nuclei
across the nuclear chart using the Energy Density Functional method and a {\it
non-empirical} pairing functional derived, without further approximation, at
lowest order in the two-nucleon vacuum interaction, including the Coulomb
force. The correlated single-particle motion is accounted for by the SLy4
semi-empirical functional. Rather unexpectedly, both neutron and proton pairing
gaps thus generated are systematically close to experimental data. Such a
result further suggests that missing effects, i.e. higher partial-waves of the
NN interaction, the NNN interaction and the coupling to collective
fluctuations, provide an overall contribution that is sub-leading as for
generating pairing gaps in nuclei. We find that including the Coulomb
interaction is essential as it reduces proton pairing gaps by up to 40%.
