111 number: Encyclopedia - 111 number

111 (number)

111 is the natural number following 110 and preceding 112.

<< 110 111 112 113 114 115 116 117 118 119 >>

List of numbers -- Integers

<< 100 110 120 130 140 150 160 170 180 190 >>

111 number - 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.

111 number - In other fields

The number 111 is sometimes called a "nelson" (particularly as a score in cricket or darts) after Admiral Nelson, who allegedly only had "One Eye, One Arm, One Ball" near the end of his life. (This is sometimes bowdlerized to say that he lost "One Eye, One Arm, One Life" during his naval career.) A score of 111 or "nelson" is considered an ill omen in cricket, because the figures "111" resemble a wicket without bails (see David Shepherd).

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

• 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

Adapted from the Wikipedia article "111 number", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki