# 113 (number)

 ← 112 113 114 →
Cardinal one hundred and thirteen
Ordinal 113th
(one hundred and thirteenth)
Factorization prime
Prime 30th
Divisors 1, 113
Roman numeral CXIII
Binary 11100012
Ternary 110123
Quaternary 13014
Quinary 4235
Senary 3056
Octal 1618
Duodecimal 9512
Vigesimal 5D20
Base 36 3536

113 (one hundred [and] thirteen) is the natural number following 112 and preceding 114. It is a prime number, so it can only be divided by one and itself.

## In mathematics

113 is the 30th prime number, following 109 and preceding 127, a Sophie Germain prime, a Chen prime and a Proth prime as it is a prime number of the form 7 × 24 + 1. 113 is an Eisenstein prime with no imaginary part and real part of the form $3n - 1$. In base 10, this prime is a primeval number, and a permutable prime with 131 and 311.

It is a highly cototient number and a centered square number. 355/113 approximates pi to six decimal places, with an error of less than 1/1133. This means that 113/355 approximates the reciprocal of pi.

## Other Fields

One hundred [and] thirteen is also: