The energy spectrum of cosmic-ray antiprotons (p's) from 0.17 to 3.5 GeV has been measured using 7886 p's detected by BESS-Polar II during a long-duration flight over Antarctica near solar minimum in December 2007 and January 2008. This shows good consistency with secondary p calculations. Cosmologically primary p's have been investigated by comparing measured and calculated p spectra. BESS-Polar II data show no evidence of primary p's from the evaporation of primordial black holes.