111 (number)

111 is the natural number following 110 and preceding 112.

Template:Numbers 110s
Cardinal	one hundred and eleven
Ordinal	111th
Factorization	$111=3\cdot 37$
Roman numeral	CXI
Binary	1101111
Hexadecimal	6F

In mathematics

One hundred eleven is R₃ or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 x 37, therefore all triplets (numbers like 222 or 666) in base ten are of the form 3n 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 (= 12433₁₀).

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.

External Links

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