  Years ago, Zeev Rudnick defined the Poisson generic real numbers by counting
the number of occurrences of long blocks of digits in the initial segments of
the expansions of the real numbers in a fixed integer base. Peres and Weiss
proved that almost all real numbers, with respect to Lebesgue measure, are
Poisson generic, but they did not publish their proof. In this note first we
transcribe Peres and Weiss' proof and then we show that there are computable
Poisson generic instances and that all Martin-L\"of random real numbers are
Poisson generic.
