We have searched for proton decay via p→e+π0 and p→μ+π0 using Super-Kamiokande data from April 1996 to March 2015, 0.306  megaton·years exposure in total. The atmospheric neutrino background rate in Super-Kamiokande IV is reduced to almost half that of phase I-III by tagging neutrons associated with neutrino interactions. The reach of the proton lifetime is further enhanced by introducing new signal criteria that select the decay of a proton in a hydrogen atom. No candidates were seen in the p→e+π0 search. Two candidates that passed all of the selection criteria for p→μ+π0 have been observed, but these are consistent with the expected number of background events of 0.87. Lower limits on the proton lifetime are set at τ/B(p→e+π0)>1.6×1034  years and τ/B(p→μ+π0)>7.7×1033  years at 90% confidence level.