This is the largest number of dimensions for which a vector-valued cross product can be defined; the cross product in this many dimensions is related to the octonions.
The discovery of exotic spheres of this dimension earned John Milnor the 2011 Abel prize. This number, the smallest double Mersenne prime, is also the fewest number of sides of a regular polygon that cannot be constructed with a compass and straightedge. This is the largest number of dimensions for which a vector-valued cross product can be defined; the cross product in this many dimensions is related to the octonions. The interior angles of a regular polygon with this many sides equals five pi radians over this number, or around 128 degrees. For 10 points, give the number of sides of a heptagon.
The discovery of exotic spheres of this dimension earned John Milnor the 2011 Abel prize.
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