  Building off of the work of Kervaire and Milnor, and Hill, Hopkins, and
Ravenel, Xu and Wang showed that the only odd dimensions n for which S^n has a
unique differentiable structure are 1, 3, 5, and 61. We show that the only even
dimensions below 140 for which S^n has a unique differentiable structure are 2,
6, 12, 56, and perhaps 4.
