# 59 (number)

 ← 58 59 60 →
Cardinal fifty-nine
Ordinal 59th
(fifty-ninth)
Factorization prime
Divisors 1, 59
Roman numeral LIX
Binary 1110112
Ternary 20123
Quaternary 3234
Quinary 2145
Senary 1356
Octal 738
Duodecimal 4B12
Vigesimal 2J20
Base 36 1N36

59 (fifty-nine) is the natural number following 58 and preceding 60.

## In mathematics

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.[1]

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:

## Notes

1. ^ H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie. The Fifty-Nine Icosahedra.
2. ^ 59 Seconds Video Festival