113 (number)

← 112 113 114 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred thirteen
Ordinal	113th (one hundred thirteenth)
Factorization	prime
Prime	30th
Divisors	1, 113
Greek numeral	ΡΙΓ´
Roman numeral	CXIII, cxiii
Binary	11100012
Ternary	110123
Senary	3056
Octal	1618
Duodecimal	9512
Hexadecimal	7116

113 (one hundred [and] thirteen) is the natural number following 112 and preceding 114.

Mathematics

113 is a prime number, a Sophie Germain prime, an emirp, an isolated prime, a Chen prime, a highly cototient number, a centered square number, and a Proth prime as it is a prime number of the form $7\times 2^{4}+1.$ 113 is also an Eisenstein prime with no imaginary part and real part of the form $3n-1$. In decimal, this prime is a primeval number and a permutable prime with 131 and 311.

113 is the denominator of 355/113, an accurate approximation to π.

$F_{7}(113)={\frac {113^{128}+1}{2}}$ is the smallest generalized Fermat prime with odd base and $k\geq 7$.

The ratio ${\frac {\pi (x)}{x/\ln x}}$, where $\pi$ is the prime-counting function, attains its maximum value of ${\frac {30\ln 113}{113}}\approx 1.255059$ at $x=113$.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134