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

The Highest Recorded Proton Spectrum at Earth since the Beginning of the Space Age