  The solar soft X-ray observations from the GOES satellites provide one of the
best quantitative records of solar activity, with nearly continuous flare
records since 1975. We present a uniform analysis of the entire time series for
1975 to 2022 at NOAA class C1 level or above, to characterize the occurrence
distribution function (ODF) of the flares observed in the 1-8 A spectral band.
The analysis includes estimations of the peak fluxes of the 12 flares that
saturated the 1-8 A time series. Our new estimates include NOAA's recently
established correction factor (1.43) to adjust the GOES-1 through GOES-15 data
covering 1975-2016. For each of the 12 saturated events we have made new
estimates of peak fluxes based on fits to the rise and fall of the flare time
profile, and have validated our extrapolation schemes by comparing with
artificially truncated but unsaturated X10-class events. SOL2003-11-04 now has
a peak flux of 4.32e-3 W/m^2. This corresponds to X43 on the new scale, or X30
on the old scale. We provide a list in the Appendix for peak fluxes of all 38
events above 10^-3 W/m^2, the GOES X10 level, including the 12 saturated
events. The full list now gives us a first complete sample from which we obtain
an occurrence distribution function (ODF) for peak energy flux , often
represented as a power law dF/dE ~ E^-alpha, for which we find alpha = 1.973 +-
0.014 in the range M1 to X3. The power-law description fails at the high end,
requiring a downward break in the ODF above the X10 level. We give a tapered
powerlaw description of the resulting CCDF (complementary cumulative
distribution function) and extrapolate it into the domain of "superflares,"
i.e. flares with bolometric energies > 10^33 erg. Extrapolation of this fit
provides estimates of 100-yr and 1000-yr GOES peak fluxes that agree reasonably
well with other such estimates using different data sets and methodology.
