We report on the yield of protons and antiprotons, as a function of centrality and transverse momentum, in Au+Au collisions at rootS(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 (p) over bar/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.