61

This number is a prime.

The great Topologist John Milnor had his conjecture disproved by M. Mahowald, who found S(61), the set of all oriented diffeomorphism classes of closed smooth homotopy 61-spheres is the trivial group. Reference: "Differential Toplogy Forty-Six Years Later", John Milnor, Notice of the AMS, June/July 2011, pp.804-809. [Post]