34 (number)
Encyclopedia
34 is the natural number
following 33
and preceding 35
.
and has four divisor
s including unity and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33, 34, 35; the next such cluster of semiprimes is 85, 86, 87.
It is the ninth Fibonacci number
and a companion Pell number
. Since it is an odd-indexed Fibonacci number, 34 is a Markov number
, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.
This number is the magic constant
of a 4 by 4 normal magic square
:
Thirty-four is a heptagonal number.
It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite
member of the 7-aliquot tree.
There is no solution to the equation φ
(x) = 34, making 34 a nontotient
. Nor is there a solution to the equation x - φ(x) = 34, making 34 a noncototient
.
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 33
33 (number)
33 is the natural number following 32 and preceding 34.-In mathematics:33 is the largest positive integer that cannot be expressed as a sum of different triangular numbers. It is also the smallest odd repdigit that is not a prime number.33 is the eighth distinct semiprime comprising the prime...
and preceding 35
35 (number)
35 is the natural number following 34 and preceding 36.- In mathematics :35 is the sum of the first five triangular numbers, making it a tetrahedral number....
.
In mathematics
34 is the ninth distinct semiprimeSemiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
and has four divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s including unity and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33, 34, 35; the next such cluster of semiprimes is 85, 86, 87.
It is the ninth Fibonacci number
Fibonacci number
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
and a companion Pell number
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers that have been known since ancient times, the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers...
. Since it is an odd-indexed Fibonacci number, 34 is a Markov number
Markov number
A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equationx^2 + y^2 + z^2 = 3xyz,\,studied by .The first few Markov numbers are...
, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.
This number is the 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 a 4 by 4 normal 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...
:
Thirty-four is a heptagonal number.
It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number....
member of the 7-aliquot tree.
There is no solution to the equation φ
Euler's totient function
In number theory, the totient \varphi of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n In number theory, the totient \varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that...
(x) = 34, making 34 a nontotient
Nontotient
In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...
. Nor is there a solution to the equation x - φ(x) = 34, making 34 a noncototient
Noncototient
In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ = n, where φ stands for Euler's totient function, has no solution for m...
.
In science
- 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 seleniumSeleniumSelenium is a chemical element with atomic number 34, chemical symbol Se, and an atomic mass of 78.96. It is a nonmetal, whose properties are intermediate between those of adjacent chalcogen elements sulfur and tellurium... - Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M34Messier 34Messier 34 is an open cluster in the constellation Perseus. It was probably discovered by Giovanni Batista Hodierna before 1654 and included by Charles Messier in his catalog of comet-like objects in 1764. Messier described it as, "A cluster of small stars a little below the parallel of γ...
, a magnitude 6.0 open clusterOpen clusterAn open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, and many more are thought to exist...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
PerseusPerseus (constellation)Perseus is a constellation in the northern sky, named after the Greek hero Perseus. It was one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and remains one of the 88 modern constellations defined by the International Astronomical Union... - The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 34, a peculiar galaxyPeculiar galaxyA peculiar galaxy is a galaxy which is unusual in its size, shape, or composition. Peculiar galaxies come about as a result of interactions between galaxies, and they may contain atypical amounts of dust or gas, may have higher or lower surface brightness than a typical galaxy, or may have...
in the constellation CetusCetusCetus is a constellation. Its name refers to Cetus, a sea monster in Greek mythology, although it is often called 'the whale' today. Cetus is located in the region of the sky that contains other water-related constellations such as Aquarius, Pisces, and Eridanus.-Ecliptic:Although Cetus is not... - The Saros number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on 1917 BC August and ended on 384 BC February. The duration of Saros series 34 was 1532.5 years, and it contained 86 solar eclipses. - The Saros number of the lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on 1633 BC May and ended on 335 BC June. The duration of Saros series 34 was 1298.1 years, and it contained 73 lunar eclipses.
In sports
- The jersey numberSquad numberIn team sports, the squad number, shirt number, jersey number, sweater number, uniform number or simply a number is the number worn on a player's uniform, to identify and distinguish each player from others wearing the same or similar uniforms...
34 has been retired by several North American sports teams in honor of past playing greats or other key figures:- In Major League BaseballMajor League BaseballMajor League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
:- The Houston AstrosHouston AstrosThe Houston Astros are a Major League Baseball team located in Houston, Texas. They are a member of the National League Central division. The Astros are expected to join the American League West division in 2013. Since , they have played their home games at Minute Maid Park, known as Enron Field...
and Texas RangersTexas Rangers (baseball)The Texas Rangers are a professional baseball team in the Dallas-Fort Worth Metroplex, based in Arlington, Texas. The Rangers are a member of the Western Division of Major League Baseball's American League, and are the reigning A.L. Western Division and A.L. Champions. Since , the Rangers have...
, both for Hall of FamerNational Baseball Hall of Fame and MuseumThe National Baseball Hall of Fame and Museum is an American history museum and hall of fame, located at 25 Main Street in Cooperstown, New York, operated by private interests serving as the central point for the study of the history of baseball in the United States and beyond, the display of...
Nolan RyanNolan RyanLynn Nolan Ryan, Jr. , nicknamed "The Ryan Express", is a former Major League Baseball pitcher. He is currently principal owner, president and CEO of the Texas Rangers....
. - The Minnesota TwinsMinnesota TwinsThe Minnesota Twins are a professional baseball team based in Minneapolis, Minnesota. They play in the Central Division of Major League Baseball's American League. The team is named after the Twin Cities area of Minneapolis and St. Paul. They played in Metropolitan Stadium from 1961 to 1981 and the...
, for Hall of Famer Kirby PuckettKirby PuckettKirby Puckett was a Major League Baseball center fielder. He played his entire 12-year baseball career with the Minnesota Twins and he is the Twins franchise's all-time leader in career hits, runs, doubles, and total bases...
. - The Oakland AthleticsOakland AthleticsThe Oakland Athletics are a Major League Baseball team based in Oakland, California. The Athletics are a member of the Western Division of Major League Baseball's American League. From to the present, the Athletics have played in the O.co Coliseum....
and Milwaukee BrewersMilwaukee BrewersThe Milwaukee Brewers are a professional baseball team based in Milwaukee, Wisconsin, currently playing in the Central Division of Major League Baseball's National League...
, both for Hall of Famer Rollie FingersRollie FingersRoland Glen Fingers is a former Major League Baseball relief pitcher. During his 18-year baseball career, he pitched for the Oakland Athletics , San Diego Padres and Milwaukee Brewers . He became only the second reliever to be elected to the National Baseball Hall of Fame in 1992...
. - Additionally, the Los Angeles DodgersLos Angeles DodgersThe Los Angeles Dodgers are a professional baseball team based in Los Angeles, California. The Dodgers are members of Major League Baseball's National League West Division. Established in 1883, the team originated in Brooklyn, New York, where it was known by a number of nicknames before becoming...
have not issued the number since the departure of Fernando ValenzuelaFernando ValenzuelaFernando Valenzuela Anguamea is a Mexican former left-handed pitcher, most notably with the Los Angeles Dodgers.In 1981, the 20-year-old Valenzuela took Los Angeles by storm, winning his first 8 decisions and leading the Dodgers to the World Championship...
following the 1990 season. Under current team policy, Valenzuela's number is not eligible for retirement because he is not in the Hall of Fame.
- The Houston Astros
- In the NBANational Basketball AssociationThe National Basketball Association is the pre-eminent men's professional basketball league in North America. It consists of thirty franchised member clubs, of which twenty-nine are located in the United States and one in Canada...
:- The Houston RocketsHouston RocketsThe Houston Rockets are an American professional basketball team based in Houston, Texas. The team plays in the Southwest Division of the Western Conference in the National Basketball Association . The team was established in 1967, and played in San Diego, California for four years, before being...
, for Hall of Famer Hakeem OlajuwonHakeem OlajuwonHakeem Abdul Olajuwon is a retired Nigerian-American professional basketball player. From 1984 to 2002, he played the center position in the National Basketball Association for the Houston Rockets and Toronto Raptors. He led the Rockets to back-to-back NBA championships in 1994 and 1995. In 2008,...
.
- The Houston Rockets
- In the NFLNational Football LeagueThe National Football League is the highest level of professional American football in the United States, and is considered the top professional American football league in the world. It was formed by eleven teams in 1920 as the American Professional Football Association, with the league changing...
:- The Chicago BearsChicago BearsThe Chicago Bears are a professional American football team based in Chicago, Illinois. They are members of the North Division of the National Football Conference in the National Football League...
, for Hall of FamerPro Football Hall of FameThe Pro Football Hall of Fame is the hall of fame of professional football in the United States with an emphasis on the National Football League . It opened in Canton, Ohio, on September 7, 1963, with 17 charter inductees...
Walter PaytonWalter PaytonWalter Jerry Payton was an American football running back who played for the Chicago Bears of the National Football League for thirteen seasons. Walter Payton was known around the NFL as "Sweetness". He is remembered as one of the most prolific running backs in the history of American football...
. - The Houston Oilers, for Hall of Famer Earl CampbellEarl CampbellEarl Christian Campbell , nicknamed The Tyler Rose, is a former professional American Football running back. He, Paul Hornung and O.J Simpson are the only people to have won the Heisman Trophy , were first overall National Football League draft picks and are in both the Pro Football Hall of Fame...
. The franchise continues to honor the number in its current incarnation as the Tennessee TitansTennessee TitansThe Tennessee Titans are a professional American football team based in Nashville, Tennessee, United States. They are members of the South Division of the American Football Conference in the National Football League . Previously known as the Houston Oilers, the team began play in 1960 as a charter...
.
- The Chicago Bears
- In Major League Baseball
In other fields
34 is also:- The traffic code of IstanbulIstanbulIstanbul , historically known as Byzantium and Constantinople , is the largest city of Turkey. Istanbul metropolitan province had 13.26 million people living in it as of December, 2010, which is 18% of Turkey's population and the 3rd largest metropolitan area in Europe after London and...
, TurkeyTurkeyTurkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe... - Rule 34 of the Internet, a memeInternet memeThe term Internet meme is used to describe a concept that spreads via the Internet. The term is a reference to the concept of memes, although the latter concept refers to a much broader category of cultural information.-Description:...
stating that "If it exists, there is pornPornographyPornography or porn is the explicit portrayal of sexual subject matter for the purposes of sexual arousal and erotic satisfaction.Pornography may use any of a variety of media, ranging from books, magazines, postcards, photos, sculpture, drawing, painting, animation, sound recording, film, video,...
of it. No exceptions." - Rule 34 (novel)Rule 34 (novel)Rule 34 is a near-future science fiction novel by Charles Stross. It is a loose sequel to Halting State, and was released on July 5 and 7th , 2011. The title is a reference to the meme Rule 34 of the Internet, a meme which states that "If it exists, there is porn of it...
, a novel by Charles StrossCharles StrossCharles David George "Charlie" Stross is a British writer of science fiction, Lovecraftian horror and fantasy. He was born in Leeds.Stross specialises in hard science fiction and space opera... - "#3434 (song)"#34" is a song by Dave Matthews Band, featured as an instrumental piece on their debut album, Under the Table and Dreaming. The song was inspired by and written for Miguel Valdez, a percussionist who collaborated with the band in 1992 and died due to hepatitis in 1993...
", a song by the Dave Matthews BandDave Matthews BandDave Matthews Band, sometimes shortened to DMB, is a U.S. rock band formed in Charlottesville, Virginia in 1991. The founding members were singer-songwriter and guitarist Dave Matthews, bassist Stefan Lessard, drummer/backing vocalist Carter Beauford and saxophonist LeRoi Moore. Boyd Tinsley was... - 34 Skidoo, the 1970s magic square puzzlePuzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
- In the title of the 1947 movie Miracle on 34th StreetMiracle on 34th StreetMiracle on 34th Street is a 1947 Christmas film written by George Seaton from a story by Valentine Davies, directed by George Seaton and starring Maureen O'Hara, John Payne, Natalie Wood and Edmund Gwenn...
, remade in 1994 - The number of the French department HéraultHéraultHérault is a department in the south of France named after the Hérault river.-History:Hérault is one of the original 83 departments created during the French Revolution on 4 March 1790...
- +34 is the code for international direct-dial phone calls to SpainSpainSpain , officially the Kingdom of Spain languages]] under the European Charter for Regional or Minority Languages. In each of these, Spain's official name is as follows:;;;;;;), is a country and member state of the European Union located in southwestern Europe on the Iberian Peninsula...
- The lucky number of Victor PelevinVictor PelevinVictor Olegovich Pelevin is a Russian fiction writer. His books usually carry the outward conventions of the science fiction genre, but are used to construct involved, multi-layered postmodernist texts, fusing together elements of pop culture and esoteric philosophies...
's protagonist Stepan Mikhailov in the novel Numbers, published as part of DTT(NN) [Dialectics in Times of Transition (from Nowhere into Nothing)] - Request for productionRequest for productionA request for production is a legal request for documents, electronically stored information, or other tangible items. In civil procedure, during the discovery phase of litigation, a party to a lawsuit may request that another party provide any documents that it has that pertain to the subject...
, Rule 34 of the U.S. Federal Rules of Civil ProcedureFederal Rules of Civil ProcedureThe Federal Rules of Civil Procedure govern civil procedure in United States district courts. The FRCP are promulgated by the United States Supreme Court pursuant to the Rules Enabling Act, and then the United States Congress has 7 months to veto the rules promulgated or they become part of the...
.
External links
- Prime Curios! 34 from the Prime PagesPrime pagesThe Prime Pages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin.The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms...