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Real space DFT (RSDFT) is a simulation technique most suitable for massively-parallel architectures to perform first-principles electronic-structure calculations based on density functional theory. We here report unprecedented simulations on the electron states of silicon nanowires with up to 107,292 atoms carried out during the initial performance evaluation phase of the K computer being developed at RIKEN. The RSDFT code has been parallelized and optimized so as to make effective use of the various capabilities of the K computer. Simulation results for the self-consistent electron states of a silicon nanowire with 10,000 atoms were obtained in a run lasting about 24 hours and using 6,144 cores of the K computer. A 3.08 peta-flops sustained performance was measured for one iteration of the SCF calculation in a 107,292-atom Si nanowire calculation using 442,368 cores, which is 43.63% of the peak performance of 7.07 peta-flops.