On the Crossing Number of K_13

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.