On the crossing number of K13K13

Since the crossing number of K12K12 is now known to be 150, it is well-known that simple counting arguments and Kleitman's parity theorem for the crossing number of K2n+1K2n+1 combine with a specific drawing of K13K13 to show that the crossing number of K13K13 is one of the numbers in {217,219,221,223,225}{217,219,221,223,225}. We show that the crossing number is not 217.