  We present algorithms giving upper and lower bounds for the number of
independent primitive rational Vassiliev invariants of degree m modulo those of
degree m-1. The values have been calculated for the formerly unknown degrees m
= 10, 11, 12. Upper and lower bounds coincide, which reveals that all Vassiliev
invariants of degree smaller 13 are orientation insensitive and are coming from
representations of Lie algebras so and gl. Furthermore, a conjecture of Vogel
is falsified and it is shown that the \Lambda-module of connected trivalent
diagrams (Chinese characters) is not free.
