 111 (number)

111 Cardinal one hundred [and] eleven Ordinal 111th
(one hundred [and] eleventh)Numeral system 111 Factorization Divisors 1, 3, 37, 111 Roman numeral CXI Binary 1101111_{2} Octal 157_{8} Duodecimal 93_{12} Hexadecimal 6F_{16} 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 Canadian and British English. Occasionally it is referred to as "eleventyone", particularly by hobbits.^{[1]}
Contents
In mathematics
111 is a perfect totient number.
111 is R_{3} 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 111_{2} = 7_{10}. 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 (= 12433_{10}).
In radix 18 the number 111 is the third power of seven 7^{3} (= 343_{10}) which is the only radix where 111 is a 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 sixbysix 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 nQueens Problem for n = 6. It is also an nonagonal number.
In base 10, it is a Harshad number.
Nelson
Main article: Nelson (cricket)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. (Which is in fact incorrect  Nelson never lost a leg.)
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 1,1,1Trichloroethane 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.
 A nonemergency medical public helpline on trial in England; see NHS 111.
 "eleventyone" is satirized Internet slang for overexclamation in typed statements.^{[citation needed]}
 A musical movement.
See also
References
 ^ John Ronald Reuel Tolkien (1993). The fellowship of the ring: being the first part of The lord of the rings. HarperCollins. ISBN 9780261102354. http://books.google.com/books?id=VUi4RAAACAAJ. Retrieved 29 August 2011.
 Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134
External links
Categories: Horatio Nelson
 Integers
 Superstitions
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