113 (number)

113 is a natural number that follows 112 and precedes 114. It is a prime number, meaning it cannot be divided evenly except by 1 and itself.

The Roman numeral form is CXIII. In binary it is 1110001. The sum of its digits (1+1+3) is 5, so it is not divisible by 3 or 9.

Properties of mathematics

113 belongs to the earlier prime numbers. It is also a permutable prime: all rearrangements of its digits—113, 131, and 311—are themselves prime numbers. Because 311 is prime and different from 113, it also falls into the category of emirps, which are prime numbers whose reversal is also prime.

When 113 is multiplied by 2 and 1 is added, the result is 227, which is also prime; this property makes 113 a Sophie Germain prime. It is also a number greater than 100 that cannot be divided evenly, making it a typical example used to test primality algorithms.

113 and the measurement of pi

113 is notable as the denominator of the fraction 355/113, which is a very close approximation of pi. This approximation is known as the Zŭ Chōngzhī method (Milü), and its accuracy extends to several decimal places beyond the fraction, making it a useful method for hand calculation.

Use in other languages and nomenclature

The number 113 also designates the atomic number of flerovium in the periodic table, whose official name was set as 'nihonium' (symbol Nh). Some countries, notably Italy and Norway, use 113 as an emergency telephone number. The uses and practices associated with this number vary from country to country.