[en] We report the first measurements of the kurtosis (κ), skewness (S), and variance (σ²) of net-proton multiplicity (N_p-N_p) distributions at midrapidity for Au+Au collisions at √(s_NN)=19.6, 62.4, and 200 GeV corresponding to baryon chemical potentials (μ_B) between 200 and 20 MeV. Our measurements of the products κσ² and Sσ, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long-range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the √(s_NN) dependence of κσ². From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for μ_B below 200 MeV.