111 (number)

← 110 111 112 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred eleven
Ordinal	111th (one hundred and eleventh)
Factorization	3 × 37
Divisors	1, 3, 37, 111
Roman numeral	CXI
Binary	11011112
Ternary	110103
Quaternary	12334
Quinary	4215
Senary	3036
Octal	1578
Duodecimal	9312
Hexadecimal	6F16
Vigesimal	5B20
Base 36	3336

111 (One hundred [and] eleven) is the natural number following 110 and preceding 112.

In mathematics

111 is a perfect totient number.

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. As a repunit, it also follows that 111 is a palindromic number.

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 128: 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, 99, 101, 105, 110, 111, 117, 119 (sequence A002384 in OEIS)

In base 18, the number 111 is 7³ (= 343₁₀) which is the only base where 111 is a perfect power.

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:

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

(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.^[1] It is also an nonagonal number.

In base 10, it is a Harshad number.

Nelson

The number 111 is sometimes called "a Nelson" after Admiral Nelson, who allegedly only had "One Eye, One Arm, One Leg" near the end of his life. This is in fact inaccurate - Nelson never lost a leg. Alternate meanings include "One Eye, One Arm, One Ambition" and "One Eye, One Arm, One Arsehole".

It is particularly known as a score in cricket. A score of 111 or multiples thereof (222 = "double nelson", 333 = "triple nelson" and so on) is considered unlucky by some in English cricket: most famously by the international umpire David Shepherd, who had a whole retinue of peculiar mannerisms - hops, shuffles, jiggles and so on - that he would indulge in if the score was ever a "Nelson" multiple. Particularly if the number of wickets also matched - 111/1, 222/2 etc.

In other fields

111 is also:

• The atomic number of the element roentgenium (Rg).
• The chemical compound 1,1,1-Trichloroethane is a chlorinated hydrocarbon that was used as an industrial solvent with a trade name "Solvent 111".
• The emergency telephone number in New Zealand; see 111 (emergency telephone number).
• A non-emergency medical public helpline operating in England and Scotland; see NHS 111.
• It is the lowest positive integer requiring six syllables to name in American English, or seven syllables (including "and") in Canadian and British English.
• Occasionally it is referred to as "eleventy-one", as read in The Fellowship of the Ring by J.R.R. Tolkien.^[2]

See also

• List of highways numbered 111

References

1. "Sloane's A006003 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. John Ronald Reuel Tolkien (1993). The fellowship of the ring: being the first part of The lord of the rings. HarperCollins. ISBN 978-0-261-10235-4. Retrieved 29 August 2011.

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

External links

• The Number 111 at the VirtueScience Database of Number Correlations
• The 111 Experience of J'lahn