Number reference
59 explained.
59: fifty-nine, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- fifty-nine
- Classification
- prime
- Factors
- 1, 59
- Prime factorization
- 59
- Square root
- 7.681146
- Cube root
- 3.892996
- Binary
- 111011
- Octal
- 73
- Hexadecimal
- 3B
- Roman numeral
- LIX
- Digit sum
- 14
- Digital root
- 5
What makes 59 notable
- Prime. 59 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
59 in everyday use
Fifty-nine is the largest number that appears on a clock's minute or second display, since the next tick rolls over to the hour. It is the atomic number of praseodymium, a rare-earth metal used in aircraft alloys and the green of some glass. In Coxeter's classic 1938 study The Fifty-Nine Icosahedra, 59 is the number of stellations of the icosahedron.
Fifty-nine is the seventeenth prime and a twin prime with 61. It is a safe prime, because (59 − 1) / 2 = 29 is also prime. It is the sum of three consecutive primes, 17 + 19 + 23. Fifty-nine leaves a remainder of 3 when divided by 4, so it is not a sum of two squares, and in binary it is 111011.
Nearby numbers
How to read this page
Because 59 is prime, the factor list stops at 1 and 59 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 59 in its prime factorisation inherits it from here.
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