# 111 number

**111** is the natural number following 110 and preceding 112.

Template:Numbers 110s | |

Cardinal | one hundred and eleven |

Ordinal | 111th |

Factorization | |

Roman numeral | CXI |

Binary | 1101111 |

Hexadecimal | 6F |

## In mathematics

**One hundred eleven** is R_{3} or the second repunit, a number like 11, 111, or 1111 that consists of **rep**eated **unit**s, or 1's. It equals 3 x 37, therefore all triplets (numbers like 222 or 666) in base ten are of the form 3*n* x 37.

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. "111" is not prime in base ten, but is prime in base two, where 111 = 7 in base ten. It is also prime in these other bases 3 to 100: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, and 99. 111 is also prime in base 111 (= 12433_{10}).

The smallest magic square using only prime numbers (and 1) has a magic constant of 111:

31 73 7 13 37 61 67 1 43

A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111:

24 16 33 23 10 5 11 15 28 8 13 36 20 14 2 31 25 19 1 18 6 29 27 30 21 22 7 17 32 12 34 26 35 3 4 9

(The square has this magic constant because 1+2+3+...+34+35+36 = 666, and 666 / 6 = 111).

This number is also the magic constant of n-Queens Problem for n = 6, an enneagonal number and a Harshad number.

**111** is the lowest positive integer requiring six syllables to name in American English, or seven syllables (including "and") in British English.

## In other fields

The number 111 is sometimes called a "nelson", after Admiral Nelson.

**One hundred eleven** is also:

- The atomic number of an element called roentgenium (Rg). The permanent name was assigned in November 2004 and replaces the temporary name unununium (Uuu).
- A Swissair route until Swissair Flight 111
- Considered an ill omen as a score in cricket, because the figures "111" resemble a wicket without bails.
- The emergency telephone number in New Zealand; see 1-1-1.
- The year AD
**111**or 111 BC. **Eleventy-one**, the age at which Bilbo Baggins leaves the Shire in J.R.R. Tolkien's*The Lord of the Rings*

## External links

- One being's lifelong connection to 111 http://www.the111experience.org

es:Ciento once fr:111 (nombre) ko:111 it:Centoundici ja:111 ru:111 (число) sl:111 (število) sv:111 (tal)