  The probability of occurrence of extreme solar particle events (SPEs) with
the fluence of (>30 MeV) protons F30>10^{10} cm^{-2} is evaluated based on data
of cosmogenic isotopes 14C and 10Be in terrestrial archives
centennial-millennial time scales. Four potential candidates with
F30=(1-1.5)x10^{10} cm^{-2} and no events with F30>2x10^{10} cm^{-2} are
identified since 1400 AD in the annually resolved 10Be data. A strong SPE
related to the Carrington flare of 1859 AD is not supported by the data. For
the last 11400 years, 19 SPE candidates with F30=(1-3)x10^{10} cm^{-2} are
found and clearly no event with F30>5x10^{10} cm^{-2} (50-fold the SPE of
23-Feb-1956) occurring. This values serve as an observational upper limit for
the strength of SPE on the time scale of tens of millennia. Two events, ca. 780
and 1460 AD, appear in different data series making them strong candidates to
extreme SPEs. We built a distribution of the occurrence probability of extreme
SPEs, providing a new strict observational constraint. Practical limits can be
set as F30~1x, 2-3x, and 5x10^{10} cm^{-2} for the occurrence probability
~10^{-2}, 10^{-3} and 10^{-4} year^{-1}, respectively. Because of
uncertainties, our results should be interpreted as a conservative upper limit
of the SPE occurrence near Earth. The mean SEP flux is evaluated as ~40 (cm2
sec)^{-1} in agreement with estimates from the lunar rocks. On average, extreme
SPEs contribute about 10% to the total SEP fluence.
