We present the largest-volume (425 Mpc/h=607 Mpc on a side) full radiative transfer simulation of cosmic reionization to date. We show that there is significant additional power in density fluctuations at very large scales. We systematically investigate the effects this additional power has on the progress, duration and features of reionization, as well as on selected reionization observables. We find that comoving simulation volume of ~100 Mpc/h per side is sufficient for deriving a convergent mean reionization history, but that the reionization patchiness is significantly underestimated. We use jackknife splitting to quantify the convergence of reionization properties with simulation volume for both mean-density and variable-density sub-regions. We find that sub-volumes of ~100 Mpc/h per side or larger yield convergent reionization histories, except for the earliest times, but smaller volumes of ~50 Mpc/h or less are not well converged at any redshift. Reionization history milestones show significant scatter between the sub-volumes, of Delta z=0.6-1 for ~50 Mpc/h volumes, decreasing to Delta z=0.3-0.5 for ~100 Mpc/h volumes, and $Delta z$~0.1 for ~200 Mpc/h volumes. If we only consider mean-density sub-regions the scatter decreases, but remains at Delta z~0.1-0.2 for the different size sub-volumes. Consequently, many potential reionization observables like 21-cm rms, 21-cm PDF skewness and kurtosis all show good convergence for volumes of ~200 Mpc/h, but retain considerable scatter for smaller volumes. In contrast, the three-dimensional 21-cm power spectra at large scales (k<0.25 h/Mpc) do not fully converge for any sub-volume size. These additional large-scale fluctuations significantly enhance the 21-cm fluctuations, which should improve the prospects of detection considerably, given the lower foregrounds and greater interferometer sensitivity at higher frequencies. (abridged)
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