360

This number is a composite.

(360 repeated 360 times) * 2^360 + 360 - 1 is prime. [Noll]

Bryant Tuckerman found the Mersenne prime M₁₉₉₃₇ using an IBM360.

The 360-sided regular polygon is the only one in which the angles (in degrees) are prime, i.e., 179. [Petrov]

(There is one curio for this number that has not yet been approved by an editor.)