The PHOBOS experiment has measured the charged particle multiplicity at midrapidity in Au+Au collisions at sqrt[SNN]=200 GeV as a function of the collision centrality. Results on dNch/dη||η|<1;1 divided by the number of participating nucleon pairs 〈Npart〉/2 are presented as a function of 〈Npart〉. As was found from similar data at sqrt[SNN]=130 GeV the data can be equally well described by parton saturation models and two-component fits, which include contributions that scale as Npart and the number of binary collisions Ncoll. We compare the data at the two energies by means of the ratio R200/130 of the charged particle multiplicity for the two different energies as a function of 〈Npart〉. For events with 〈Npart〉> 100, we find that this ratio is consistent with a constant value of 1.14±0.01(stat)±0.05(syst).