We report on the yield of protons and antiprotons, as a function of centrality and transverse momentum, in Au+Au collisions at sqrt[s(NN)]=200 GeV measured at midrapidity by the PHENIX experiment at the BNL Relativistic Heavy Ion Collider. In central collisions at intermediate transverse momenta (1.5<p(T)<4.5 GeV/c) a significant fraction of all produced particles are protons and antiprotons. They show a centrality-scaling behavior different from that of pions. The pmacr;/pi and p/pi ratios are enhanced compared to peripheral Au+Au, p+p, and e(+)e(-) collisions. This enhancement is limited to p(T)<5 GeV/c as deduced from the ratio of charged hadrons to pi(0) measured in the range 1.5<p(T)<9 GeV/c.