  This work aims at a systematic investigations of the pairing properties and
Fermi properties from the proton drip-line to the neutron drip-line. In order
to provide more accurate mass formula with skyrme SKI3 force, the global
descriptive power of the SKI3-HFB model for pairing properties are made in this
study. Systematic Skyrme SKI3-Hartree-Fock-Bogoliubov calculations with a mixed
volume-surface pairing force are carried out to study the ground-state neutron
and proton pairing gap, neutron and proton pairing energy and neutron and
proton Fermi energy for about 2095 even-even nuclei ranging from $2\le{Z}\le110
$ to $2\le{N}\le236$. The calculated results of neutron and proton pairing gap
are compared with experimental data using the difference-point formulas
$\Delta^{(3)}, \Delta^{(4)}$ and $\Delta^{(5)}$, and also compared with the
neutron and proton pairing gap of Lipkin-Nogami model. It is shown that the
Skyrme-SKI3 functional with the mixed volume-surface pairing force can be
successfully used for describing the ground-state pairing and Fermi properties
of the investigated nuclei, in particularly the neutron-rich nuclei and the
exotic nuclei near the neutron drip-line. On the other hand, the calculated
neutron and proton pairing gap are in good agreement with the available
experimental values of the neutron and proton pairing gap of the
difference-point formulas $\Delta^{(3)}, \Delta^{(4)}$ and $\Delta^{(5)}$ and
with the data of Lipkin-Nogami model over the whole nuclear chart.
