Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. Since 15! + 1 is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime.

It is also a highly cototient number.

There are 59 stellations of the icosahedron.

59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13# + 1 = 2 × 3 × 5 × 7 × 11 × 13 + 1 = 59 × 509.

Fifty-nine is:

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