We study nonnegative classical solutions u of the polyharmonic inequality

-Dmu = 0 in B1(0) - {0} ? Rn,

where D is the Laplacian operator. We give necessary and sufficient conditions on integers n = 2 and m = 1 such that these solutions u satisfy a pointwise a priori bound as x? 0. In this case we show that the optimal bound for u is

u(x) = O(G(x)) as x? 0

where G is the fundamental solution of Laplacian in Rn.