111 (One hundred
ndeleven) is the natural number following
110 and preceding
112.
In mathematics
111 is a
perfect totient number.
111 is R
3 or the second
repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recrea ...
, a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers ...
like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like
222
__NOTOC__
Year 222 (Roman numerals, CCXXII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Antoninus and Severus (or, less ...
or 777) in
base ten are of the form 3''n'' × 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
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one).
The base-2 numeral system is a positional notatio ...
, where 111
2 = 7
10. 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
In
base 18
There are many different numeral systems, that is, writing systems for expressing numbers.
By culture / time period
By type of notation
Numeral systems are classified here as to whether they use positional notation (also known as place-value ...
, the number 111 is 7
3 (= 343
10) which is the only base where 111 is a
perfect power
In mathematics, a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a higher integer power of another integer greater than one. More formally, ''n' ...
.
The smallest
magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
using only 1 and
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...
s has a magic constant of 111:
A six-by-six
magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
using the numbers 1 to 36 also has a
magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
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 a
nonagonal number.
In base 10, it is a
Harshad number
In mathematics, 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 in base are also known as -harshad (or -Niven) numbers.
Harshad numbe ...
as well as a
strobogrammatic number
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A strobogrammatic ...
.
Nelson
In 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. 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".
Particularly in
cricket
Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by st ...
, multiples of 111 are called a double Nelson (222), triple Nelson (333), quadruple Nelson (444; also known as a salamander) and so on.
A score of 111 is considered by some to be unlucky. To combat the supposed bad luck, some watching lift their feet off the ground. Since an umpire cannot sit down and raise his feet, the international umpire
David Shepherd had a whole retinue of peculiar mannerisms if the score was ever a Nelson multiple. He would hop, shuffle, or jiggle, particularly if the number of wickets also matched—111/1, 222/2 etc.
In other fields
111 is also:
*The
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of the element
roentgenium (Rg).
*The
chemical compound
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one ele ...
1,1,1-trichloroethane
The organic compound 1,1,1-trichloroethane, also known as methyl chloroform, is a chloroalkane. This colorless, sweet-smelling liquid was once produced industrially in large quantities for use as a solvent. It is regulated by the Montreal Prot ...
is a
chlorinated
In chemistry, halogenation is a chemical reaction that entails the introduction of one or more halogens into a compound. Halide-containing compounds are pervasive, making this type of transformation important, e.g. in the production of polym ...
hydrocarbon
In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and hydrophobic, and their odors are usually weak or ...
that was used as an industrial
solvent
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
with a trade name "Solvent 111".
*The
emergency telephone number
Most public switched telephone networks have a single emergency telephone number (sometimes known as the universal emergency telephone number or the emergency services number) that allows a caller to contact local emergency services for assista ...
in
New Zealand
New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 List of islands of New Zealand, smaller islands. It is the ...
; see
111 (emergency telephone number)
111 (usually pronounced ''one-one-one'') 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 i ...
.
*
NHS 111
111 is a free-to-call single non-emergency number medical helpline operating in England, Scotland and parts of Wales. The 111 phone service has replaced the various non-geographic 0845 rate numbers and is part of each country's National Health ...
, a medical helpline in England and Scotland.
*It is the lowest positive integer requiring seven syllables to name in
English (British and Commonwealth), or six syllables (by dropping the "and") in
American English
American English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the United States and in most circumstances ...
.
*Occasionally it is referred to as "
eleventy-one", as read in ''
The Fellowship of the Ring'' by
J.R.R. Tolkien
John Ronald Reuel Tolkien (, ; 3 January 1892 – 2 September 1973) was an English writer and philologist. He was the author of the high fantasy works '' The Hobbit'' and '' The Lord of the Rings''.
From 1925 to 1945, Tolkien was the Ra ...
.
*The first Pacific (
4-6-2
Under the Whyte notation for the classification of steam locomotives, represents the wheel arrangement of four leading wheels on two axles, six powered and coupled driving wheels on three axles and two trailing wheels on one axle. The loco ...
) locomotive in Great Britain was the
Great Western Railway's No. 111 The Great Bear of 1908, designed by
George Jackson Churchward
George Jackson Churchward (31 January 1857 – 19 December 1933) was an English railway engineer, and was chief mechanical engineer of the Great Western Railway (GWR) in the United Kingdom from 1902 to 1922.
Early life
Churchward was born at ...
. This locomotive was rebuilt into a
4-6-0 Castle Class engine in 1924, renamed
Viscount Churchill, and retained the fleet number 111 until scrapped in July 1953.
*In
Pakistan
Pakistan ( ur, ), officially the Islamic Republic of Pakistan ( ur, , label=none), is a country in South Asia. It is the world's List of countries and dependencies by population, fifth-most populous country, with a population of almost 24 ...
i history,
Pakistan Army
The Pakistan Army (, ) is the Army, land service branch of the Pakistan Armed Forces. The roots of its modern existence trace back to the British Indian Army that ceased to exist following the partition of India, Partition of British India, wh ...
's
111 Brigade is notorious for being used for staging the
coups to overthrow the elected governments in order to impose
martial law
Martial law is the imposition of direct military control of normal civil functions or suspension of civil law by a government, especially in response to an emergency where civil forces are overwhelmed, or in an occupied territory.
Use
Marti ...
.
See also
*
List of highways numbered 111
References
Notes
*Wells, D. ''
The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 134
External links
{{DEFAULTSORT:111 (Number)
Horatio Nelson
Integers