  Several groups have reported a possible excess of primary electrons at high
energies with the joint fit of the positron fraction and total
electron/positron spectra. With the latest release of high-precision
electron/positron spectra measured by AMS-02, we further confirm this excess by
fitting $\Delta\Phi$ $\rm(i.e., \Phi_{e^-}-\Phi_{e^+})$ data in this work. Then
we investigate the contribution of a single nearby supernova remnant to the
primary electron excess and find that Monogem can reasonably account for this
excess. Moreover, we predict that the electron spectrum may harden again at a
few TeVs due to Vela's contribution. DAMPE, which can accurately measure
electrons at TeV scale, is expected to provide the robust test of this new
spectral feature in the near future. Finally, we fit the proton spectrum data
of DAMPE with Monogem or Loop I. We find that both the primary electron excess
and the proton spectral bump could be mainly generated by Monogem.
