  Because the production cross sections of gamma-rays, electrons, and positrons
made in p-p collisions, $\sigma_{pp\rightarrow \gamma}$ and
$\sigma_{pp\rightarrow {e}^\pm}$, respectively, are kinematically equivalent
with respect to the parent pion-production cross section $\sigma_{pp\rightarrow
\pi}$, we obtain $\sigma_{pp\rightarrow {e}^\pm}$ directly from the machine
data on $\sigma_{pp\rightarrow \gamma}$. In Sato et al. (2012), we give
explicitly $\sigma_{pp\rightarrow \gamma}$, reproducing quite well the
accelerator data with LHC, namely $\sigma_{pp\rightarrow {e}^\pm}$ is
applicable enough over the wide energy range from GeV to 20\,PeV for projectile
proton energy. We dicuss in detail the relation between the cross sections, and
present explicitly $\sigma_{pp\rightarrow {e}^\pm}$ that are valid into the PeV
electron energy.
