  The origin of relativistic electrons in the Crab nebula which are producing
the broad-band flat radio spectrum of this prototype plerion has proved
difficult to understand. Here I show that these electrons can be naturally
explained as a relic population of the pulsar wind electrons that have lost
most of their energy in the expanding nebula because of intensive radiative and
adiabatic cooling in the past. The observed radio spectrum suggests that the
initial slowing-down time of the pulsar was about 30 yrs (or less), which
implies that it has been born with a spin period P_0 ~ 3-5 ms, several times
shorter than presently believed. Consistency of these results with the current
data and the historical records is discussed.
