  Since the crossing number of K_{12} is now known to be 150, it is well-known
that simple counting arguments and Kleitman's parity theorem for the crossing
number of K_{2n+1} combine with a specific drawing of K_{13} to show that the
crossing number of K_{13} is one of the numbers in {217,219,221,223,225}. We
show that the crossing number is not 217.
