111 (number)

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<< 110 111 112 113 114 115 116 117 118 119 >> List of numbers — Integers << 100 110 120 130 140 150 160 170 180 190 >>
Cardinal <td>one hundred and eleven
Ordinal	111th
Factorization <td><math>3 \cdot 37</math>
Roman numeral	CXI
Binary	1101111
Hexadecimal	6F

111 (One hundred (and) eleven) is the natural number following 110 and preceding 112. It is the lowest positive integer requiring six syllables to name in American English, or seven syllables (including "and") in British English.

[edit] In mathematics

111 is R₃ or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are of the form 3n × 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 111₂ = 7₁₀. It is also prime in these other bases up 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 1 and prime numbers 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).

111 is also the magic constant of the n-Queens Problem for n = 6. It is also an enneagonal number.

In base 10, it is a Harshad number and a Zuckerman number.

[edit] 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.) Another suggestion is that the number is derived from his three great victories, thus Copenhagen, Nile & Trafalgar which gives the sequence "Won - Won - Won".

A score of 111 or multiples thereof (called "double nelson", "triple nelson" etc.) is considered an ill omen in cricket, because the figures "111" resemble a wicket without bails. Some people, most notably David Shepherd, develop superstitions around nelsons.

In the United Kingdom of the "pre-decimal" days, some bank cashiers used the term a "Nelson" for an amount of one pound, one shilling and one penny (£1 1s 1d).

111 is also:

The atomic number of the element 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