Number 31 | by PlayWork Mug

31 is the number of regular polygons with an odd number of sides that are known to be constructible with compass and straightedge. 31 is the third Mersenne prime (25 − 1)[1] and the eighth Mersenne prime exponent, as well as the fourth primorial prime, and together with twenty-nine, a primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496, since 496 = 2(5 − 1)(25 − 1). 31 is also the 4th lucky prime[2] and the 11th supersingular prime.[3] 31 is a centered triangular number,[4] the first prime centered pentagonal number[5] and a centered decagonal number.[6] 31 is the eighth happy number.[7] For the Steiner tree problem, 31 is the number of possible Steiner topologies for Stein...