  Glitches are sudden spin-up events that punctuate the steady spin down of
pulsars and are thought to be due to the presence of a superfluid component
within neutron stars. The precise glitch mechanism and its trigger, however,
remain unknown. The size of glitches is a key diagnostic for models of the
underlying physics. While the largest glitches have long been taken into
account by theoretical models, it has always been assumed that the minimum size
lay below the detectability limit of the measurements. In this paper we define
general glitch detectability limits and use them on 29 years of daily
observations of the Crab pulsar, carried out at Jodrell Bank Observatory. We
find that all glitches lie well above the detectability limits and by using an
automated method to search for small events we are able to uncover the full
glitch size distribution, with no biases. Contrary to the prediction of most
models, the distribution presents a rapid decrease of the number of glitches
below ~0.05 $\mu$Hz. This substantial minimum size indicates that a glitch must
involve the motion of at least several billion superfluid vortices and provides
an extra observable which can greatly help the identification of the trigger
mechanism. Our study also shows that glitches are clearly separated from all
the other rotation irregularities. This supports the idea that the origin of
glitches is different to that of timing noise, which comprises the unmodelled
random fluctuations in the rotation rates of pulsars.
