  We solve a problem of Komeda concerning the proportion of numerical
semigroups which do not satisfy Buchweitz' necessary criterion for a semigroup
to occur as the Weierstrass semigroup of a point on an algebraic curve. We also
show that the family of semigroups known to be Weierstrass semigroups using a
result of Eisenbud and Harris, has zero density in the set of all semigroups.
In the process, we prove several more general results about the structure of a
typical numerical semigroup.
