The proton-proton interaction at very small distances is studied by analyzing the elastic scattering data near 2 and 3 GeV. The explicit inclusion of the one-pion-exchange contribution in the high-angular-momentum states and that from the one-boson exchange in the intermediate-angular-momentum states together with the assumption that the absorption coefficients can be represented by a smooth function of the orbital angular momentum l allowed us to determine the phase shifts for lower-angular-momentum states. Three independent solutions have been found at each energy considered, which are smoothly connected with solutions at lower energies. The form of the absorption is such that in general its maximum is in the 1D2 state. With respect to the real phase shifts, all of the solutions are consistent with the presence of a strongly repulsive core in the 1S0 state, and solutions have been found which suggest a repulsive core also in the triplet odd states. The strong spin dependence of the interaction is stressed and this is also discussed in connection with the forward scattering amplitude. Predictions of several triple scattering parameters are given which may eliminate the ambiguity of the solutions found.