59 (number)

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Cardinal fifty-nine
Ordinal 59th
(fifty-ninth)
Factorization prime
Divisors 1, 59
Greek numeral ΝΘ´
Roman numeral LIX
Binary 1110112
Ternary 20123
Quaternary 3234
Quinary 2145
Senary 1356
Octal 738
Duodecimal 4B12
Hexadecimal 3B16
Vigesimal 2J20
Base 36 1N36

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

In mathematics

Fifty-nine is the 17th prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime,[1] a safe prime[2] and the 14th supersingular prime.[3] 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.[4]

It is also a highly cototient number.[5]

There are 59 stellations of the icosahedron.[6]

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 = 30031.

59 is the highest integer a single symbol may represent in the Sexagesimal system.

Fifty-nine is:

References

1. ^ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
6. ^ H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie. The Fifty-Nine Icosahedra.
7. ^ Richard Poe, "Parts of the Rosary", TheChantRosary.com, 2-4-2018
8. ^ 59 Seconds Video Festival