Fibrillary protein aggregates rich beta-sheet structure have been implicated in the pathology of several neurodegenerative diseases. In this work, we investigate the formation of fibrils by performing discontinuous molecular dynamics simulations on systems containing 12 to 96 model Ac-KA(14)K-NH2 peptides using our newly developed off-lattice, implicit-solvent, intermediate-resolution model, PRIME. We find that, at a low concentration, random-coil peptides assemble into a-helices at low temperatures. At intermediate concentrations, random-coil peptides assemble into cc-helices at low temperatures and large beta-sheet structures at high temperatures. At high concentrations, the system forms beta-sheets over a wide range of temperatures. These assemble into fibrils above a critical temperature which decreases with concentration and exceeds the isolated peptide's folding temperature, At very high temperatures and all concentrations, the system is in a random-coil state. All of these results are in good qualitative agreement with those by Blondelle and co-workers on Ac-KA14K-NH2 peptides. The fibrils observed in our simulations mimic the structural characteristics observed in experiments in terms of the number of sheets formed, the values of the intra- and intersheet separations, and the parallel peptide arrangement within each beta-sheet. Finally, we find that when the strength of the hydrophobic interaction between nonpolar side chains is high compared to the strength of hydrogen bonding, amorphous aggregates, rather than fibrillar aggregates, are formed.