  We present a set of generators of the full annihilator ideal for the Witt
ring of an arbitrary field of characteristic unequal to two satisfying a
non-vanishing condition on the powers of the fundamental ideal in the torsion
part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This
result could only be proved by first obtaining a new lower bound on the 2-adic
valuation of Stirling numbers of the second kind.
