GaN nanowires have been grown without external catalyst on Si(111) substrates by plasma-assisted molecular beam epitaxy. Nanowire aspect ratios (length/diameter) of about 250 have been achieved. During the initial stage of the growth, there is a nucleation process in which the number of wires increases and the most probable nucleation diameter of about 10nm has been observed, which slowly increases with deposition time. For deposition time longer than the nucleation stage, the nanowire length as a function of diameter monotonically decreases. This phenomenon can be explained by adatom diffusion on the nanowire lateral surface towards the tip.