  Let $c(K)$ denote the crossing number of a knot $K$ and let $K_1\# K_2$
denote the connected sum of two oriented knots $K_1$ and $K_2$. It is a very
old unsolved question that whether $c(K_1\# K_2)=c(K_1)+c(K_2)$. In this paper
we show that $c(K_1\# K_2)> (c(K_1)+c(K_2))/16$.
