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

| ||||
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Cardinal | one hundred thirteen | |||

Ordinal | 113th (one hundred thirteenth) | |||

Factorization | prime | |||

Prime | 30th | |||

Divisors | 1, 113 | |||

Greek numeral | ΡΙΓ´ | |||

Roman numeral | CXIII | |||

Binary | 1110001_{2} | |||

Ternary | 11012_{3} | |||

Octal | 161_{8} | |||

Duodecimal | 95_{12} | |||

Hexadecimal | 71_{16} |

- 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]}a Chen prime^{[2]}and a Proth prime as it is a prime number of the form 7 × 2^{4}+ 1. 113 is also an Eisenstein prime with no imaginary part and real part of the form . In base 10, this prime is a primeval number,^{[3]}and a permutable prime with 131 and 311. - 113 is at the junction between a large cluster of primes and a large gap in primes. It is the end of the prime sextuplet (97, 101, 103, 107, 109, 113), the next one of which does not occur till 16057–16073. It is at the beginning of a large prime gap, 113–127, which is not surpassed until 523–541.
- 113 is a highly cototient number
^{[4]}and a centered square number.^{[5]} - 355/113 approximates π to six decimal places, with an error of less than 1/113
^{3}. This means that 113/355 approximates the reciprocal of π. - 113 is the smallest positive integer that cannot be represented in the Four fours problem using standard rules. It can be solved using the gamma function.
^{[clarification needed]}^{[dubious – discuss]}

- 113, the atomic number of the element nihonium
- Cadmium-113m, a radioisotope and nuclear isomer with a halflife of 14.1 years

113 is:

- The fire emergency telephone number in Indonesia
- The intelligence agency telephone number in Iran
- The medical emergency telephone number in Latvia and Norway
- The police emergency telephone number in Italy, Luxembourg, Slovenia, and Vietnam
- The time telephone number in Argentina
- The suicide line in the Netherlands

- 113 (band), a French hip hop group
- 113, the port number of the IDENT Internet protocol that helps identify the user of a particular TCP connection
- The A113 easter egg from Pixar movies.
- 113, in enduro, is regarded as an unlucky number to be given to a race entrant and is colloquially known as a "blind pew"

**^**"Sloane's A005384 : Sophie Germain primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A109611 : Chen primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A072857 : Primeval numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A100827 : Highly cototient numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.**^**"Sloane's A001844 : Centered square numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-26.

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