  The recent solar minimum activity period and the consequent minimum
modulation conditions for cosmic rays were unusual compared to previous solar
minimum periods. The highest spectra of galactic protons (and other cosmic
rays) were recorded by the PAMELA instrument at Earth in late 2009, in contrast
to expectations. The spectrum, between 100 MeV and 50 GeV, for December 2009 is
compared to proton spectra observed during previous solar minimum periods, back
to 1965. Corresponding numerical modeling is presented which predicts that the
next solar minimum spectra could even be higher if similar modulation
conditions then would occur as in 2008-2009. The reason is that incorporating
gradient and curvature drifts in modulation models causes proton spectra for A
> 0 solar magnetic cycles (e.g., around 1976, 1997) to always be higher than
during A < 0 cycles (e.g. around 1965, 1987, 2009) at energies below a few GeV,
if the same modulation conditions would prevail.
