  How big were the first planetesimals? We attempt to answer this question by
conducting coagulation simulations in which the planetesimals grow by mutual
collisions and form larger bodies and planetary embryos. The size frequency
distribution (SFD) of the initial planetesimals is considered a free parameter
in these simulations, and we search for the one that produces at the end
objects with a SFD that is consistent with asteroid belt constraints. We find
that, if the initial planetesimals were small (e.g. km-sized), the final SFD
fails to fulfill these constraints. In particular, reproducing the bump
observed at diameter D~100km in the current SFD of the asteroids requires that
the minimal size of the initial planetesimals was also ~100km. This supports
the idea that planetesimals formed big, namely that the size of solids in the
proto-planetary disk ``jumped'' from sub-meter scale to multi-kilometer scale,
without passing through intermediate values. Moreover, we find evidence that
the initial planetesimals had to have sizes ranging from 100 to several 100km,
probably even 1,000km, and that their SFD had to have a slope over this
interval that was similar to the one characterizing the current asteroids in
the same size-range. This result sets a new constraint on planetesimal
formation models and opens new perspectives for the investigation of the
collisional evolution in the asteroid and Kuiper belts as well as of the
accretion of the cores of the giant planets.
