113 (number)
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Short description: Natural number
| ||||
---|---|---|---|---|
Cardinal | one hundred thirteen | |||
Ordinal | 113th (one hundred thirteenth) | |||
Factorization | prime | |||
Prime | 30th | |||
Divisors | 1, 113 | |||
Greek numeral | ΡΙΓ´ | |||
Roman numeral | CXIII | |||
Binary | 11100012 | |||
Ternary | 110123 | |||
Quaternary | 13014 | |||
Quinary | 4235 | |||
Senary | 3056 | |||
Octal | 1618 | |||
Duodecimal | 9512 | |||
Hexadecimal | 7116 | |||
Vigesimal | 5D20 | |||
Base 36 | 3536 |
113 (one hundred [and] thirteen) is the natural number following 112 and preceding 114.
Mathematics
- 113 is the 30th prime number (following 109 and preceding 127), so it can only be divided by one and itself. 113 is a Sophie Germain prime,[1] an emirp, an isolated prime, a Chen prime[2] and a Proth prime as it is a prime number of the form [math]\displaystyle{ 7\times 2^{4}+1. }[/math] 113 is also an Eisenstein prime with no imaginary part and real part of the form [math]\displaystyle{ 3n - 1 }[/math]. In decimal, this prime is a primeval number[3] and a permutable prime with 131 and 311.
- 113 is a highly cototient number[4] and a centered square number.[5]
- 113 is the denominator of 355/113, an accurate approximation to π.
See also
- 113 (disambiguation)
- A113 is a Pixar recurring inside joke or Easter Egg, e.g.: (WALL-E) = (W-A113).
References
- ↑ "Sloane's A005384 : Sophie Germain primes". OEIS Foundation. https://oeis.org/A005384.
- ↑ "Sloane's A109611 : Chen primes". OEIS Foundation. https://oeis.org/A109611.
- ↑ "Sloane's A072857 : Primeval numbers". OEIS Foundation. https://oeis.org/A072857.
- ↑ "Sloane's A100827 : Highly cototient numbers". OEIS Foundation. https://oeis.org/A100827.
- ↑ "Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844.
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134
Original source: https://en.wikipedia.org/wiki/113 (number).
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