30 (thirty) is the

_{8} has ^{''n''}''m'', where ''p'' does not divide ''m'', has a subgroup of order ''p''^{''n''}, and 30 is the only number less than 60 that is not either a prime or of the above form, it is the only candidate for the order of a

Report of the 7 July Review Committee

Accessed 18 Dec 2011

{{DEFAULTSORT:30 (Number)
Integers

natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathematical terminology, w ...

following 29 and preceding 31.
In mathematics

Thirty is the sum of the first four squares, which makes it asquare pyramidal number
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...

.
It is a primorial
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

.
It is a pronic number
A pronic number is a number which is the product of two consecutive integer
An integer (from the Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoke ...

.
30 is the smallest sphenic number In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number the ...

, and the smallest of the form , where ''r'' is a prime greater than 3. 30 has an aliquot sum
In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number th ...

of 42; the second sphenic number In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number the ...

and all sphenic numbers In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number the ...

of this form have an aliquot sum
In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number th ...

12 greater than themselves.
Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number
In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number th ...

.
30 is the largest number such that all coprime
In number theory, two integer
An integer (from the Latin wikt:integer#Latin, ''integer'' meaning "whole") is colloquially defined as a number that can be written without a Fraction (mathematics), fractional component. For example, 21, 4, 0, ...

s smaller than itself, except for 1, are prime
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 ...

.
A polygon
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

with thirty sides is called a triacontagon
In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 (number), 5040 degrees.
Regular triacontagon
The ''regular polygon, regular triacontagon'' is a constructible polygon, by an ...

.
The icosahedron
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

and the dodecahedron
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

are Platonic solid
In three-dimensional space, a Platonic solid is a Regular polyhedron, regular, Convex set, convex polyhedron. It is constructed by Congruence (geometry), congruent (identical in shape and size), regular polygon, regular (all angles equal and all sid ...

s with 30 edges. The icosidodecahedron
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

is an Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex polytope, convex Uniform polyhedron, uniform polyhedra composed of regular polygons meeting in identical vertex (geometry), vertices, ...

with 30 vertices, and the Tutte–Coxeter graph
In the mathematics, mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth (graph theory), girth ...

is a symmetric graph
In the mathematics, mathematical field of graph theory, a Graph (discrete mathematics), graph ''G'' is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices ''u''1—''v''1 and ''u''2—''v''2 of ''G'', there is an Graph autom ...

with 30 vertices.
''E''Coxeter number
In mathematics, the Coxeter number ''h'' is the order (group theory), order of a Coxeter element of an irreducible Coxeter group. It is named after H.S.M. Coxeter.
Definitions
Note that this article assumes a finite Coxeter group. For infinite Cox ...

30.
30 is a Harshad number
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...

in base 10.
Since any group ''G'' such that , ''G'', = ''p''simple group
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

less than 60 that one needs other methods to reject.
In science

* Theatomic number
The atomic number or proton number (symbol ''Z'') of a chemical element
In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. ...

of zinc
Zinc is a chemical element
In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical element ...

is 30.
Astronomy

*Messier object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters'').
Because Messier was only int ...

M30, a magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (mathematics), the relative size of an object
*Norm (mathematics), a term for the size or length of a vector
*Order of ...

8.5 globular cluster
A globular cluster is a sphere, spherical collection of stars. wiktionary:globular, Globular clusters are very tightly bound by gravity, with a high concentration of stars towards their centers. Their name is derived from Latin —a small sphere. ...

in the constellation
A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate object.
The origins of the earliest ...

Capricornus
Capricornus is one of the constellation
A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an i ...

* The New General Catalogue
The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue
Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural scien ...

object , a double star in the constellation Pegasus
Pegasus ( gr, Πήγασος, ''Pḗgasos''; la, Pegasus, Pegasos) is a mythical
Myth is a folklore genre
Folklore is the expressive body of culture shared by a particular group of people; it encompasses the traditions common to t ...

Age 30

* The minimum age for United States senators. * In some regions of the continental United States, the 30th birthday is celebrates by gifting sticks.In other fields

Thirty is: * Used (as –30–) to indicate the end of a newspaper (or broadcast) story, a copy editor's typographical notation * The number of days in the months April, June, September and November (and in unusual circumstances February—seeFebruary 30
Several non-standard dates are used in calendars. Some are used sarcastically, some for scientific or mathematical purposes, and some for exceptional or fictional calendars.
January 0
January 0 or 0 January is an alternative name for December 31. ...

)
* The total number of major and minor keys in Western tonal music
Tonality is the arrangement of pitch (music), pitches and/or chord (music), chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triad (music), triadi ...

, including enharmonic equivalents
* In years of marriage, the pearl wedding anniversary
A wedding anniversary is the anniversary
An anniversary is the date on which an event took place or an institution was founded in a previous year, and may also refer to the commemoration or celebration of that event. For example, the first ...

* The duration in years of the Thirty Years' War
The Thirty Years' War was a conflict fought largely within the Holy Roman Empire
The Holy Roman Empire ( la, Sacrum Romanum Imperium; german: Heiliges Römisches Reich) was a multi-ethnic complex of territories in Western Europe, Weste ...

- 1618 to 1648
* The code for international direct dial
Country calling codes or country dial-in codes are telephone number
A telephone number is a sequence of digits assigned to a fixed-line telephone subscriber station connected to a telephone line or to a wireless electronic telephony device ...

phone calls to Greece
Greece ( el, Ελλάδα, Elláda, ), officially the Hellenic Republic, is a country located in Southeastern Europe
Southeast Europe or Southeastern Europe () is a geographical subregion
A subregion is a part of a larger region
In geogr ...

* The house number of 30 St Mary Axe
30 St Mary Axe (known previously as the Swiss Re
Swiss Reinsurance Company Ltd,

" Swiss Re. Retrieved on 18 Jan ...

(The Gherkin)
* The number of tracks on " Swiss Re. Retrieved on 18 Jan ...

The Beatles
The Beatles were an English rock
Rock most often refers to:
* Rock (geology)
A rock is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by the minerals included, its Chemical compou ...

' eponymous album
An album is a collection of audio recordings issued as a collection on compact disc (CD), Phonograph record, vinyl, audio tape, or another medium. Albums of recorded sound were developed in the early 20th century as individual Phonograph rec ...

, usually known as ''The White Album
''The Beatles'', also known colloquially as the White Album, is the ninth studio album by the English Rock music, rock band the Beatles, released on 22 November 1968. It stands as the only Double Album, double album released by the band. Featu ...

''
* A stage in young adulthood
* Part of the name of:
** 30 Odd Foot of Grunts
Russell Ira Crowe (born 7 April 1964) is an actor, director, musician, and singer. He was born in New Zealand, spent 10 years of his childhood in Australia, and moved there permanently at age 21. He came to international attention for his role ...

, the band fronted by actor Russell Crowe
** The movie title '' 13 Going on 30'', starring Jennifer Garner
Jennifer Anne Garner (born April 17, 1972) is an American actress. Born in Houston
Houston ( ) is the List of cities in Texas by population, most populous city in Texas, List of United States cities by population, fourth-most populous c ...

** The title of the Food Network
Food Network is an American basic cable channel owned by Television Food Network, G.P., a joint venture and general partnership between Discovery, Inc. (which holds a 69% ownership stake of the network) and Nexstar Media Group (which owns the re ...

show ''30 Minute Meals
''30 Minute Meals'' is a Food Network
Food Network is an American basic cable channel owned by Television Food Network, G.P., a joint venture
A joint venture is a business entity created by two or more parties, generally characterized by s ...

''
** ''30 Days of Night
''30 Days of Night'' is a three-issue horror fiction, horror comic book Limited series (comics), miniseries written by Steve Niles, illustrated by Ben Templesmith, and published by American company IDW Publishing in 2002. All three parties co-own ...

'', a comic book miniseries and film
A film, also called a movie, motion picture or moving picture, is a work of visual art
The visual arts are art forms such as painting
Painting is the practice of applying paint
Paint is any pigmented liquid, liquefiable, ...

* Judas Iscariot
Judas Iscariot (; he, יהודה איש-קריות , "Judah, man of KeriothKerioth ( he, קְרִיּוֹת, ''Kriyot'') is the name of two cities mentioned in the Hebrew Bible. The spelling Kirioth appears in the King James Version of Amos ...

betrayed Jesus
Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew
Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it ...

for 30 pieces of silver
Thirty pieces of silver was the price for which Judas Iscariot
Judas Iscariot (; he, יהודה איש-קריות , "Judah, man of KeriothKerioth ( he, קְרִיּוֹת, ''Kriyot'') is the name of two cities mentioned in the Hebrew Bibl ...

( Matthew 26:15)
* The number of the French department Gard
Gard () is a department
Department may refer to:
* Departmentalization, division of a larger organization into parts with specific responsibility
Government and military
*Department (country subdivision), a geographical and administrative divis ...

* Number of letters in Bulgarian alphabet
The Bulgarian alphabet is used to write the Bulgarian language #REDIRECT Bulgarian language #REDIRECT Bulgarian language
Bulgarian (, ; bg, label=none, български, bălgarski, ) is a South Slavic languages, South Slavic language spok ...

* Number of letters in Serbian alphabet
* 30 was the route number of the bus blown up by terrorists in Tavistock Square
Tavistock Square is a public square
In Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euc ...

during the 7 July 2005 London bombings
The 7 July 2005 London bombings, often referred to as 7/7, were a series of coordinated Islamist suicide attack
right , Several coordinated suicide attacks targeted the United States on September 11, 2001
A suicide attack is any violent ...

Accessed 18 Dec 2011

History and literature

* At about age 30 (according to Luke 3:23),Jesus
Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew
Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it ...

of Nazareth was baptized by John the Baptist
John the Baptist ''Yohanān HaMatbil''; la, Ioannes Baptista; grc-gre, Ἰωάννης ὁ βαπτιστής, ''Iōánnēs ho baptistḗs'' or , ''Iōánnēs ho baptízōn'', or , ''Iōánnēs ho pródromos'';Wetterau, Bruce. ''World history' ...

, signaling the beginning of his public ministry of teaching and healing. It was also the age when David
David (; ) (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". is described in th ...

became King (2 Samuel 5:4) and Ezekiel
Ezekiel (; he, יְחֶזְקֵאל ''Yĕḥezqēʾl'' ; in the Septuagint
The Greek Old Testament, or Septuagint (, ; from the la, septuaginta, lit=seventy; often abbreviated ''70''; in Roman numerals, LXX), is the earliest extant Koine ...

and John the Baptist began their own ministries, (based on Ezekiel 1:1 and John the Baptist's age in comparison to Jesus.)
* Age 30 is when Jewish priests traditionally start their service (according to Numbers 4:3).
* One of the rallying-cries of the 1960s student/youth protest movement was the slogan, ' Don't trust anyone over thirty'.
* In ''The Myth of Sisyphus
''The Myth of Sisyphus'' (french: link=no, Le Mythe de Sisyphe) is a 1942 philosophical essay by Albert Camus
Albert Camus ( , ; ; 7 November 1913 – 4 January 1960) was a French philosopher, author, and journalist. He won the Nobel Prize ...

'' the French existentialist Albert Camus
Albert Camus ( , ; ; 7 November 1913 – 4 January 1960) was a French philosopher, author, and journalist. He won the Nobel Prize in Literature
)
, image = Nobel Prize.png
, caption =
, awarded_for = Outstanding contributions in ...

comments that the age of thirty is a crucial period in the life of a man, for at that age he gains a new awareness of the meaning of time.
* In Franz Kafka
Franz Kafka (3 July 1883 – 3 June 1924) was a German-speaking
The German language (, ) is a West Germanic language mainly spoken in Central Europe
Central Europe is the central region of Europe. Central Europe includes contigu ...

's novel ''The Trial'' Joseph wakes up on the morning of his thirtieth birthday to find himself under arrest for an unspecified crime. After making many futile attempts to find the nature of the crime or the name of his accuser, Joseph dies on the eve of his thirty-first birthday.
* The number of uprights that formed the Sarsen Circle at Stonehenge
Stonehenge is a prehistoric monument on Salisbury Plain in Wiltshire, England, west of Amesbury. It consists of an outer ring of vertical sarsen standing stones, each around high, wide, and weighing around 25 tons, topped by connecting ho ...

, also the supposed number of holes forming the arrays of Y and Z Holes at Stonehenge.
* Western Christianity's most prolific 20th-century essayist, F. W. Boreham in 'Life at Thirty' ('Cliffs of Opal') mentions that in addition to Jesus commencing ministry at 30 (Luke 3:23), Joseph was 30 when he stood before Pharaoh, King of Egypt (Genesis 41:46), King David was 30 when he began to reign (2 Samuel 5:4), and the Levites were numbered from the age of 30 and upward (1 Chronicles 23:3). Also in that essay Boreham writes 'It was said of he English poetKeats, that "he ensphered himself in thirty perfect years and died, not young".'
Sports

* In tennis, the number 30 represents the second point gained in a game. * In baseball, 30 is the number of teams inMajor League Baseball
Major League Baseball (MLB) is a professional baseball
Professional baseball is organized baseball in which players are selected for their talents and are paid to play for a specific team or club system. It is played in baseball league, leag ...

.
* In basketball, there are 30 teams in the National Basketball Association
The National Basketball Association (NBA) is a professional basketball sports league, league in North America. The league is composed of 30 teams (29 in the United States and 1 in Canada) and is one of the four major professional sports leagu ...

.
Music

* The number of variations in Bach'sGoldberg Variations
The ''Goldberg Variations'', BWV 988, is a musical composition for keyboard by Johann Sebastian Bach
Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known f ...

* '' 30'', a 2001 album by Harry Connick, Jr.
* Thirty Seconds to Mars
Thirty Seconds to Mars (commonly stylized as 30 Seconds to Mars) is an American Rock music, rock band from Los Angeles, California, formed in 1998. The band consists of brothers Jared Leto (lead vocals, guitar, bass, keyboards) and Shannon Leto ...

, an American rock band
* " 30 Minutes", a song by t.A.T.u
* ''Thirty
30 (thirty) 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 total order, ordering (as in "this is the ''third'' largest city in the country"). I ...

'', a 2013 album by Anthony Callea
* '' XXX'', an album by Danny Brown
See also

*List of highways numbered 30
The following highways are numbered 30:
International
* AH30, Asian Highway 30
* European route E30
Australia
* Albany Highway (State Route 30, Western Australia)
Brazil
* BR-030
Canada
*Alberta Highway 30 (defunct)
*British Columbia Highway 3 ...

References