111 (number)
Encyclopedia
111 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 "eleventy
-one", particularly by hobbit
s.
.
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).
In radix 18 the number 111 is the third power of seven 73 (= 34310) which is the only radix where 111 is a power.
The smallest magic square
using only 1 and prime number
s has a magic constant of 111:
A six-by-six magic square
using the numbers 1 through 36 also has a magic constant
of 111:
(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 nonagonal number.
In base 10, it is a Harshad number
.
, 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.
110 (number)
110 is the natural number following 109 and preceding 111.It is also known as "eleventy", a term made famous by linguist and author J. R. R...
and preceding 112
112 (number)
112 is the natural number following 111 and preceding 113.-In mathematics:One hundred [and] twelve is an abundant number and a heptagonal number...
. It is the lowest positive integer requiring six syllables to name in American English
American English
American English is a set of dialects of the English language used mostly in the United States. Approximately two-thirds of the world's native speakers of English live in the United States....
, or seven syllables (including "and") in Canadian and British English
British English
British English, or English , is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere...
. Occasionally it is referred to as "eleventy
110 (number)
110 is the natural number following 109 and preceding 111.It is also known as "eleventy", a term made famous by linguist and author J. R. R...
-one", particularly by hobbit
Hobbit
Hobbits are a fictional diminutive race who inhabit the lands of Middle-earth in J. R. R. Tolkien's fiction.Hobbits first appeared in the novel The Hobbit, in which the main protagonist, Bilbo Baggins, is the titular hobbit...
s.
In mathematics
111 is a perfect totient numberPerfect totient number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers;...
.
111 is R3 or the second repunit
Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler...
, a number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222
222 (number)
222 is the natural number following 221 and preceding 223. It is a repdigit composite number, and its factorization makes it a sphenic number. It is also a Harshad number....
or 777) in base ten
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
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
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
, 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).
In radix 18 the number 111 is the third power of seven 73 (= 34310) which is the only radix where 111 is a power.
The smallest magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
using only 1 and prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s has a magic constant of 111:
| 31 | 73 | 7 |
| 13 | 37 | 61 |
| 67 | 1 | 43 |
A six-by-six magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
using the numbers 1 through 36 also has a magic constant
Magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....
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
666 (number)
666 is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and sixty-six) is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and...
, and 666 / 6 = 111).
111 is also the magic constant of the n-Queens Problem
Eight queens puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal...
for n = 6. It is also an nonagonal number.
In base 10, it is a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
.
Nelson
The number 111 is sometimes called "a Nelson" after Admiral NelsonHoratio Nelson, 1st Viscount Nelson
Horatio Nelson, 1st Viscount Nelson, 1st Duke of Bronté, KB was a flag officer famous for his service in the Royal Navy, particularly during the Napoleonic Wars. He was noted for his inspirational leadership and superb grasp of strategy and unconventional tactics, which resulted in a number of...
, 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
Cricket
Cricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...
. 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
David Shepherd (umpire)
David Robert Shepherd MBE was one of the cricket world's best-known umpires. He stood in 92 Test matches, the last of them in June 2005, and officiated in three World Cup finals.- Playing career :...
, 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 numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of the element roentgeniumRoentgeniumRoentgenium is a synthetic radioactive chemical element with the symbol Rg and atomic number 111. It is placed as the heaviest member of the group 11 elements, although a sufficiently stable isotope has not yet been produced in a sufficient amount that would confirm this position as a heavier...
(Rg). - The chemical compoundChemical compoundA chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...
1,1,1-Trichloroethane1,1,1-TrichloroethaneThe organic compound 1,1,1-trichloroethane, also known as methyl chloroform, is a chloroalkane. This colourless, sweet-smelling liquid was once produced industrially in large quantities for use as a solvent...
is a chlorinatedChlorineChlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...
hydrocarbonHydrocarbonIn organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons from which one hydrogen atom has been removed are functional groups, called hydrocarbyls....
that was used as an industrial solventSolventA solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...
with a trade name "Solvent 111". - The emergency telephone numberEmergency telephone numberMany countries' public telephone networks have a single emergency telephone number, sometimes known as the universal emergency telephone number or occasionally the emergency services number, that allows a caller to contact local emergency services for assistance. The emergency telephone number may...
in New ZealandNew ZealandNew Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...
; see 1-1-11-1-1111 is the emergency telephone number in New Zealand. It was first implemented in Masterton and Carterton on 29 September 1958, and was progressively rolled out nationwide with the last exchanges converting in 1988...
. - A non-emergency medical public helpline on trial in England; see NHS 111NHS 111 (England)NHS 111 is an English medical helpline, with a free to call three digit number, currently in pilot stage in three areas across England, and due to be rolled out nationally by 2013, at which point it will replace the NHS Direct 0845 4647 number which has been running since 1998...
. - "eleventyone" is satirized Internet slang for over-exclamation in typed statements.
- A musical movement.