163 (one hundred ndsixty-three) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following 162 and preceding 164.

In mathematics

163 is a

strong prime In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory. Definition in number theory In number theory, a strong prime is a prime number t ...

in the sense that it is greater than the arithmetic mean of its two neighboring primes. 163 is a

lucky prime In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...

and a

fortunate number A Fortunate number, named after Reo Fortune, is the smallest integer ''m'' > 1 such that, for a given positive integer ''n'', ''p'n''# + ''m'' is a prime number, where the primorial ''p'n''# is the product of the first ''n'' prime numbers. ...

. 163 is a strictly non-palindromic number, since it is not palindromic in any base between base 2 and base 161. Given 163, the

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...

returns 0, it is the fourth prime with this property, the first three such primes are 2, 101 and 149. 163 figures in an approximation of π, in which

\pi \approx  \approx 3.1411

. 163 figures in an approximation of ''e'', in which

e \approx  \approx 2.7166\dots

. 163 is a

Heegner number In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factoriza ...

, the largest of the nine such numbers. That is, the

ring of integers In mathematics, the ring of integers of an algebraic number field K is the ring of all algebraic integers contained in K. An algebraic integer is a root of a monic polynomial with integer coefficients: x^n+c_x^+\cdots+c_0. This ring is often deno ...

of the

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

\mathbb(\sqrt)

has

unique factorization In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is a ...

for

a=163

. The only other such integers are

a = 1, 2, 3, 7, 11, 19, 43, 67

. 163 is the number of -independent McKay-Thompson series for the

monster group In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order 246320597611213317192329314147 ...

. This fact about 163 might be a clue for understanding

monstrous moonshine In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group ''M'' and modular functions, in particular, the ''j'' function. The term was coined by John Conway and Simon P. Norton in 1979. ...

. 163 is a

permutable prime A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to study th ...

base 12 The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead wr ...

, which it is written as 117, the

permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

s of its digits are 171 and 711, the two numbers in base 12 are 229 and 1021 in base 10, both of which are prime. The function

f(n) = n^2 + n + 41

gives prime values for all values of

n

between 0 and 39, and for

n < 10^7

approximately half of all values are prime. 163 appears as a result of solving

f(n)=0

, which gives

n = (-1+ \sqrt ) / 2

\sqrt

appears in the

Ramanujan constant In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factoriz ...

, since -163 is a

quadratic nonresidue In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic no ...

to modulo all the primes 3, 5, 7, ..., 37. In which

e^

almost equals the integer 262537412640768744 = 640320³ + 744.

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...

famously asserted that this identity was exact in a 1975 April Fools' hoax in ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

''; in fact the value is 262537412640768743.99999999999925007259...

In astronomy

* 163 Erigone is a dark

Main belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...

asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

, the namesake of the

Erigone family An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. An ...

of asteroids

In the US military

* was a

United States Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage ...

tanker ship during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

* was a diesel-electric

submarine A submarine (or sub) is a watercraft capable of independent operation underwater. It differs from a submersible, which has more limited underwater capability. The term is also sometimes used historically or colloquially to refer to remotely op ...

during World War II * was a United States Navy during World War II * was a United States Navy ''Trefoil''-class concrete barge during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy following World War II * was a commercial

yacht A yacht is a sailing or power vessel used for pleasure, cruising, or racing. There is no standard definition, though the term generally applies to vessels with a cabin intended for overnight use. To be termed a , as opposed to a , such a pleasu ...

during

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

* was a United States Navy during World War I * 163rd Fighter Squadron, a unit of the

Indiana Air National Guard The Indiana Air National Guard (IN ANG) is the aerial militia of the State of Indiana, United States of America. It is, along with the Indiana Army National Guard, an element of the Indiana National Guard. As state militia units, the units in ...

, flies the

F-16C/D Fighting Falcon A large number of variants of the General Dynamics F-16 Fighting Falcon have been produced by General Dynamics, Lockheed Martin, and various licensed manufacturers. The details of the F-16 variants, along with major modification programs and der ...

In sports

Russ Howell Russell Wayne Howell (born September 1949) is a professional skateboarder. While working towards his degree in physical education, Howell competed and won many freestyle skateboarding competitions throughout his skating career. Life and career ...

at the

Long Beach, California Long Beach is a city in Los Angeles County, California. It is the 42nd-most populous city in the United States, with a population of 466,742 as of 2020. A charter city, Long Beach is the seventh-most populous city in California. Incorporate ...

World Championship in 1977 performed a world record 163 full rotations in

freestyle skateboarding tricks A freestyle skateboarding trick is a trick performed with a skateboard while freestyle skateboarding. Some of these tricks are done in a stationary position, unlike many other skateboarding tricks. The keys to a good freestyle contest run are var ...

* In

darts Darts or dart-throwing is a competitive sport in which two or more players bare-handedly throw small projectile point, sharp-pointed projectile, missiles known as dart (missile), darts at a round shooting target, target known as a #Dartboard, dar ...

, 163 is the lowest number that cannot be shot with three darts on a standard dart board

In transportation

Peugeot Type 163 The Peugeot Type 163 and associated models were produced from 1919 to 1924 by Peugeot. The car's engine placed it in the 10 CV class. Background Peugeot returned to passenger car production after the war slightly less rapidly than Paris based Ren ...

automobile produced from 1919 to 1924 *

Messerschmitt Me 163 The Messerschmitt Me 163 Komet is a rocket-powered interceptor aircraft primarily designed and produced by the German aircraft manufacturer Messerschmitt. It is the only operational rocket-powered fighter aircraft in history as well as ...

Komet was a German

rocket-powered A rocket-powered aircraft or rocket plane is an aircraft that uses a rocket engine for propulsion, sometimes in addition to airbreathing jet engines. Rocket planes can achieve much higher speeds than similarly sized jet aircraft, but typicall ...

fighter aircraft Fighter aircraft are fixed-wing military aircraft designed primarily for air-to-air combat. In military conflict, the role of fighter aircraft is to establish air superiority of the battlespace. Domination of the airspace above a battlefield ...

. during

* Intervale Avenue –163rd Street subway station,

Bronx, New York The Bronx () is a Boroughs of New York City, borough of New York City, coextensive with Bronx County, in the U.S. state, state of New York (state), New York. It is south of Westchester County, New York, Westchester County; north and east of the ...

subway station on the

IRT White Plains Road Line The White Plains Road Line is a rapid transit line of the A Division of the New York City Subway serving the central Bronx. It is mostly elevated and served both subway and elevated trains until 1952. The original part of the line, the part op ...

of the

New York City Subway The New York City Subway is a rapid transit system owned by the government of New York City and leased to the New York City Transit Authority, an affiliate agency of the state-run Metropolitan Transportation Authority (MTA). Opened on October 2 ...

in the USA. * 163rd Street–Amsterdam Avenue station on the

IND Eighth Avenue Line The IND Eighth Avenue Line is a rapid transit line in New York City, United States, and is part of the B Division of the New York City Subway. Opened in 1932, it was the first line of the Independent Subway System (IND), and the ''Eighth Avenu ...

of the

in America. * The Bunche Park

Metrorail METRORail is the light rail system in Houston, Texas (United States). In , the system had a ridership of , or about per weekday as of . METRORail ranks as the second most-traveled light rail system in the Southern United States and the 12th ...

station in Bunche Park, Florida, United States, at Northwest 163rd Street and 27th Avenue, set to open in 2014 * Saudi Arabian Airlines Flight 163 caught fire at

Riyadh Riyadh (, ar, الرياض, 'ar-Riyāḍ, lit.: 'The Gardens' Najdi pronunciation: ), formerly known as Hajr al-Yamamah, is the capital and largest city of Saudi Arabia. It is also the capital of the Riyadh Province and the centre of the R ...

's International Airport en route from

Karachi, Pakistan Karachi (; ur, ; ; ) is the most populous city in Pakistan and 12th most populous city in the world, with a population of over 20 million. It is situated at the southern tip of the country along the Arabian Sea coast. It is the former cap ...

on August 19, 1980 *

Iraqi Airways Flight 163 Iraqi Airways Flight 163 was a Boeing 737, Boeing 737-270C, registered YI-AGJ, that was Aircraft hijacking, hijacked in 1986. On 25 December 1986, en route from Baghdad's Saddam International Airport to Amman, Jordan, Flight 163 was hijacked by ...

, en route from

Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...

Baghdad International Airport Baghdad International Airport , previously Saddam International Airport ( ar, مطار بغداد الدولي, Maṭār Baġdād ad-Dawaliyy) is Iraq's largest international airport, located in a suburb about west of downtown Baghdad in the ...

Amman Amman (; ar, عَمَّان, ' ; Ammonite language, Ammonite: 𐤓𐤁𐤕 𐤏𐤌𐤍 ''Rabat ʻAmān'') is the capital and largest city of Jordan, and the country's economic, political, and cultural center. With a population of 4,061,150 a ...

Jordan Jordan ( ar, الأردن; tr. ' ), officially the Hashemite Kingdom of Jordan,; tr. ' is a country in Western Asia. It is situated at the crossroads of Asia, Africa, and Europe, within the Levant region, on the East Bank of the Jordan Rive ...

, was

hijacked Hijacking may refer to: Common usage Computing and technology * Bluejacking, the unsolicited transmission of data via Bluetooth * Brandjacking, the unauthorized use of a company's brand * Browser hijacking * Clickjacking (including ''like ...

and crashed on December 25, 1986 *

List of highways numbered 163 The following highways are numbered 163: Brazil * BR-163 Canada * Prince Edward Island Route 163 Costa Rica * National Route 163 (Costa Rica), National Route 163 India * National Highway 163 (India) Japan * Japan National Route 163 United St ...

In other fields

163 is also: * 163 AH is a year in the

Islamic calendar The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ, translit=al-taqwīm al-hijrī), also known in English as the Muslim calendar and Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or ...

that corresponds to 779 – 780 CE *

CD163 CD163 (Cluster of Differentiation 163) is a protein that in humans is encoded by the CD163 gene. CD163 is the high affinity scavenger receptor for the hemoglobin-haptoglobin complex and in the absence of haptoglobin - with lower affinity - for hem ...

(Cluster of Differentiation 163) is a human

protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...

encoded by the

gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...

* The Glossen Opus 163

waltz The waltz ( ), meaning "to roll or revolve") is a ballroom and folk dance, normally in triple ( time), performed primarily in closed position. History There are many references to a sliding or gliding dance that would evolve into the wa ...

Johann Strauss II Johann Baptist Strauss II (25 October 1825 – 3 June 1899), also known as Johann Strauss Jr., the Younger or the Son (german: links=no, Sohn), was an Austrian composer of light music, particularly dance music and operettas. He composed ov ...

(1855) * The number of days following the first day of

Passover Passover, also called Pesach (; ), is a major Jewish holidays, Jewish holiday that celebrates the The Exodus, Biblical story of the Israelites escape from slavery in Ancient Egypt, Egypt, which occurs on the 15th day of the Hebrew calendar, He ...

(Pesach), used to calculate the date of

Rosh Hashanah Rosh HaShanah ( he, רֹאשׁ הַשָּׁנָה, , literally "head of the year") is the Jewish New Year. The biblical name for this holiday is Yom Teruah (, , lit. "day of shouting/blasting") It is the first of the Jewish High Holy Days (, , " ...

, the Jewish New Year. * The

Burj Khalifa The Burj Khalifa (; ar, برج خليفة, , Khalifa Tower), known as the Burj Dubai prior to its inauguration in 2010, is a skyscraper in Dubai, United Arab Emirates. It is known for being the world’s tallest building. With a total height ...

in Dubai, United Arab Emirates, which is the tallest building in the world, has 163 floors.

References

* Wells, D. (1987). ''

The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, ...

'' (pp. 141–142). London: Penguin Group.

External links

*
The Number 163

The Positive Integer 163

163.com
website from

NetEase NetEase, Inc. () is a Chinese Internet technology company providing online services centered on content, community, communications, and commerce. The company was founded in 1997 by Ding Lei. NetEase develops and operates online PC and mobile game ...

The coolest number is 163

163, the Monster and Number Theory

International Brotherhood of Electrical Workers Local Union 163

Other interesting consequences of ''d''=163?
from Mathematics Stack Exchange {{DEFAULTSORT:163 (Number) Integers

In mathematics

In astronomy

In the US military

In sports

In transportation

In other fields

See also

References

External links