  Let H be a finite dimensional non-semisimple Hopf algebra over an
algebraically closed field k of characteristic 0. If H has no nontrivial
skew-primitive elements, we find some bounds for the dimension of H_1, the
second term in the coradical filtration of H. Using these results, we are able
to show that every Hopf algebra of dimension 14 is semisimple and thus
isomorphic to a group algebra or the dual of a group algebra. Also a Hopf
algebra of dimension pq where p and q are odd primes with p<q and q less than
or equal to 1 + 3p, and also less than or equal to 13, is semisimple and thus a
group algebra or the dual of a group algebra. We also have some partial results
in the classification problem for dimension 16.
