We have achieved a sustained performance of 55 TFLOPS for molecular dynamics simulations of the amyloid fibril formation of peptides from the yeast Sup35 in an aqueous solution. For performing the calculations, we used the MDGRAPE-3 system - -a special-purpose computer system for molecular dynamics simulations. Its nominal peak performance was 415 TFLOPS for Coulomb force calculations; this is the highest-ever performance reported for classical molecular dynamics simulations. Amyloid fibril formation is known to be related to the occurrence of severe diseases such as Alzheimer's, Parkinson's, and Creutzfeldt-Jakob diseases. The Sup35 protein is a "yeast prion protein," which forms mini-crystals due to aggregation; it forms an effective platform for studying the formation process of amyloid fibrils. In these simulations, we first elucidate that the amyloid-forming peptides GNNQQNY aggregate at a higher frequency than non-amyloid-forming peptides SQNGNQQRG; further, the GNNQQNY peptides tend to form parallel two-stranded -sheets that would grow into a cross- amyloid nucleus. The results are consistent with those obtained experimentally. Furthermore, we could observe an early elongation of the amyloid nucleus. This result is expected to contribute toward a deeper understanding of the amyloid growth mechanism.