Results are presented from 300 ns long atomistic molecular dynamics (MD) simulations of polyethylene (PE) melts, ranging in molecular length from C-78 to C-250. Above C-156, the self-diffusion coefficient D is seen to exhibit a clear change in its power-law dependence on the molecular weight (M), significantly deviating from a Rouse (where D similar to M-1) toward a reptation-like (where D similar to M-2.4) behavior. The mean-square displacement (msd) of chain segments and the dynamic structure factor is also calculated and the crossover from the Rouse to entangled behavior is again observed above C156. A novel strategy is also developed for projecting atomistic chain configurations to their primitive paths and thereby mapping simulation trajectories onto the reptation model. Results for the friction factor xi, the zero-shear rate viscosity eta(0) and the self-diffusion coefficient D are found to be internally consistent and in agreement with experimental rheological data.