168 (one hundred ndsixty-eight) is the natural number following 167 and preceding 169.

In mathematics

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...

, an

abundant number In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...

, and an

idoneal number In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers ''D'' such that any integer expressible in only one way as ''x''2 ± ''Dy''2 (where ''x''2 is relatively prime to ''Dy ...

. There are 168

primes 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 ways ...

less than

1000 1000 or thousand may refer to: * 1000 (number), a natural number * AD 1000, a leap year in the Julian calendar * 1000 BC, a year of the Before Christ era * 1000 metres, a middle-distance running event * 1000°, a German electronic dance music magazi ...

. 168 is the product of the first two

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. ...

s. 168 is the order of the group

PSL(2,7) In mathematics, the projective special linear group , isomorphic to , is a finite simple group that has important applications in algebra, geometry, and number theory. It is the automorphism group of the Klein quartic as well as the symmetry gro ...

, the second smallest nonabelian

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

. From

Hurwitz's automorphisms theorem In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus ''g'' > 1, stating that the number of such automorphisms ...

, 168 is the

maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given r ...

possible number of automorphisms of a genus 3

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ver ...

, this maximum being achieved by the

Klein quartic In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms ...

, whose symmetry group is PSL(2,7). The

Fano plane In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines ...

has 168

symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

. 168 is the largest known n such that 2^n does not contain all decimal digits.

In astronomy

* 168P/Hergenrother is a periodic

comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...

in the

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

* 168 Sibylla 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

In the military

* was an

Imperial Japanese Navy The Imperial Japanese Navy (IJN; Kyūjitai: Shinjitai: ' 'Navy of the Greater Japanese Empire', or ''Nippon Kaigun'', 'Japanese Navy') was the navy of the Empire of Japan from 1868 to 1945, when it was dissolved following Japan's surrend ...

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 opposing ...

* is 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 ...

fleet

tugboat A tugboat or tug is a marine vessel that manoeuvres other vessels by pushing or pulling them, with direct contact or a tow line. These boats typically tug ships in circumstances where they cannot or should not move under their own power, su ...

* 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 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 II * was a United States Navy steamer during World War II * was a La Salle-class transport during World War II

In movies

* The 168 Film Project in

Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the List of municipalities in California, largest city in the U.S. state, state of California and the List of United States cities by population, sec ...

In transportation

* New York City Subway stations **

168th Street (New York City Subway) The 168th Street station (formerly the Washington Heights–168th Street station) is an underground New York City Subway station complex shared by the IRT Broadway–Seventh Avenue Line and IND Eighth Avenue Line. It is located at the interse ...

; a subway station complex at 168th Street and Broadway consisting of: *** 168th Street (IRT Broadway – Seventh Avenue Line); serving the train ***

168th Street (IND Eighth Avenue Line) The 168th Street station (formerly the Washington Heights–168th Street station) is an underground New York City Subway station complex shared by the IRT Broadway–Seventh Avenue Line and IND Eighth Avenue Line. It is located at the inters ...

; serving the trains **

168th Street (BMT Jamaica Line) The 168th Street station was the terminal station on the demolished section of the BMT Jamaica Line in Queens, New York City. It was located between 165th and 168th Streets on Jamaica Avenue. History Early years 168th Street was part of two ...

; was the former terminal of the BMT Jamaica Line in Queens * British Rail Class 168 * VASP Flight 168 from Rio de Janeiro, Brazil to Fortaleza; crashed on June 8, 1982

In other fields

168 is also: * The year AD 168 or

168 BC __NOTOC__ Year 168 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Macedonicus and Crassus (or, less frequently, year 586 ''Ab urbe condita''). The denomination 168 BC for this year has ...

* 168 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 ...

that corresponds to

784 __NOTOC__ Year 784 ( DCCLXXXIV) was a leap year starting on Thursday of the Julian calendar. The denomination 784 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Eur ...

–

785 __NOTOC__ Year 785 ( DCCLXXXV) was a common year starting on Saturday of the Julian calendar. The article denomination 785 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent meth ...

CE * The number of hours in a

week A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are of ...

, or 7 x 24 hours * In the game of

dominoes Dominoes is a family of tile-based games played with gaming pieces, commonly known as dominoes. Each domino is a rectangular tile, usually with a line dividing its face into two square ''ends''. Each end is marked with a number of spots (also c ...

, tiles are marked with a number of spots, or pips. The Double 6 set (28 tiles) totals 168 pips *

Tracy 168 TRACY 168 (born Michael Tracy in 1958) is an American graffiti artist. He pioneered the art form known as Wildstyle. Tracy 168 came to be known as one of the most influential graffiti and street artists of all time, as variations of Wild Style writ ...

, a

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

graffiti artist *

Minuscule 168 Minuscule 168 (in the Gregory-Aland numbering), Θε31 ( Soden), is a Greek minuscule manuscript of the New Testament, on parchment. Palaeographically it has been assigned to the 13th century.K. Aland, M. Welte, B. Köster, K. Junack, "Kurzgef ...

is a

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

minuscule Letter case is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain languages. The writing ...

manuscript A manuscript (abbreviated MS for singular and MSS for plural) was, traditionally, any document written by hand – or, once practical typewriters became available, typewritten – as opposed to mechanically printed or reproduced in ...

of the

New Testament The New Testament grc, Ἡ Καινὴ Διαθήκη, transl. ; la, Novum Testamentum. (NT) is the second division of the Christian biblical canon. It discusses the teachings and person of Jesus, as well as events in first-century Chri ...

* Some

Chinese Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of ...

consider 168 a lucky number, because it is roughly homophonous with the phrase "一路發", which means "fortune all the way" * 168 is the name of the most commonly used laboratory strain of ''

Bacillus subtilis ''Bacillus subtilis'', known also as the hay bacillus or grass bacillus, is a Gram-positive, catalase-positive bacterium, found in soil and the gastrointestinal tract of ruminants, humans and marine sponges. As a member of the genus ''Bacillus ...

'', a bacterium

References

External links

Number Facts and Trivia: 168

The Number 168

The Positive Integer 168

{{DEFAULTSORT:168 (Number) Integers