31 (number)
Encyclopedia
31 is the natural number
following 30 and preceding 32.
( 25 - 1 ) as well as the fourth primorial prime
, and together with twenty-nine, another primorial prime, it comprises a twin prime
. As a Mersenne prime, 31 is related to the perfect number
496
, since 496 = 25 - 1 ( 25 - 1). 31 is the eighth Mersenne prime
exponent. 31 is also the 4th lucky prime and the 11th supersingular prime
.
31 is a centered triangular number
, a centered pentagonal number
and centered decagonal number
.
For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals.
At 31, the Mertens function sets a new low of -4, a value which is not subceded until 110
.
No integer added up to its base 10 digits results in 31, making 31 a self number
.
31 is a repdigit
in base 5 (111), and base 2 (11111).
The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime. For a time it was thought that every number of the form 3w1 would be prime. However, the next nine numbers of the sequence are composite
; their factorisations are:
The recurrence of the factor 31 in the last number above can be used to prove that no sequence of the type RwE or ERw can consist only of primes because every prime in the sequence will periodically divide further numbers. Here, 31 divides every fifteenth number in 3w1 (and 331 every 110th).
teams in honor of past playing greats:
[NASCAR]] driver Jeff Burton
drives #31, a car which was subject to a controversy when one of the sponsors changed its name after merging with another company.
In ice hockey
goaltenders often wear the number 31.
In football the number 31 has been retired by Queens Park Rangers F.C.
in memory of Ray Jones (footballer born 1988)
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 30 and preceding 32.
In mathematics
Thirty-one is the third Mersenne primeMersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
( 25 - 1 ) as well as the fourth primorial prime
Primorial prime
In mathematics, primorial primes are prime numbers of the form pn# ± 1, where:The first few primorial primes are, the largest known primorial prime is 843301# - 1 with 365,851 digits, found in 2010 by the PrimeGrid project....
, and together with twenty-nine, another primorial prime, it comprises a twin prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
. As a Mersenne prime, 31 is related to the perfect number
Perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...
496
496 (number)
Four hundred [and] ninety-six is the natural number following four hundred [and] ninety-five and preceding four hundred [and] ninety-seven.-In mathematics:...
, since 496 = 25 - 1 ( 25 - 1). 31 is the eighth Mersenne prime
Mersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
exponent. 31 is also the 4th lucky prime and the 11th supersingular prime
Supersingular prime
In mathematics, a supersingular prime is a prime number satisfying one of the following concepts:*Supersingular prime , in algebraic number theory*Supersingular prime...
.
31 is a centered triangular number
Centered triangular number
A centered triangular number is a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers...
, a centered pentagonal number
Centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers...
and centered decagonal number
Centered decagonal number
A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers...
.
For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals.
At 31, the Mertens function sets a new low of -4, a value which is not subceded until 110
110 (number)
110 is the natural number following 109 and preceding 111.It is also known as "eleventy", a term made famous by linguist and author J. R. R...
.
No integer added up to its base 10 digits results in 31, making 31 a self number
Self number
A self number, Colombian number or Devlali number is an integer which, in a given base, cannot be generated by any other integer added to the sum of that other integer's digits. For example, 21 is not a self number, since it can be generated by the sum of 15 and the digits comprising 15, that is,...
.
31 is a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
in base 5 (111), and base 2 (11111).
The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime. For a time it was thought that every number of the form 3w1 would be prime. However, the next nine numbers of the sequence are 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....
; their factorisations are:
- 333 333 331 = 1717 (number)17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...
*19607843 - 3 333 333 331 = 673*4952947
- 33 333 333 331 = 307*108577633
- 333 333 333 331 = 1919 (number)19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
*8383 (number)83 is the natural number following 82 and preceding 84.-In mathematics:Eighty-three is the sum of three consecutive primes as well as the sum of five consecutive primes ....
*211371803 - 3 333 333 333 331 = 523*3049*2090353
- 33 333 333 333 331 = 607*1511*1997*18199
- 333 333 333 333 331 = 181181 (number)181 is the natural number between 180 and 182.-In mathematics:* 181 is an odd number* 181 is a centered number** 181 is a centered pentagonal number** 181 is a centered 12-gonal number** 181 is a centered 18-gonal number...
*1841620626151 - 3 333 333 333 333 331 = 199199 (number)199 is the natural number following 198 and preceding 200.-In mathematics:* 199 is an odd number* 199 is a centered triangular number* 199 is a centered 33-gonal number* 199 is a deficient number, as 1 is less than 199* 199 is a Lucas number...
*16750418760469 - 33 333 333 333 333 331 = 31*1499*717324094199.
The recurrence of the factor 31 in the last number above can be used to prove that no sequence of the type RwE or ERw can consist only of primes because every prime in the sequence will periodically divide further numbers. Here, 31 divides every fifteenth number in 3w1 (and 331 every 110th).
Astronomy
- 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...
M31Andromeda GalaxyThe Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...
, a magnitude 4.5 galaxyGalaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
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....
AndromedaAndromeda (constellation)Andromeda is a constellation in the northern sky. It is named after Andromeda, the princess in the Greek legend of Perseus who was chained to a rock to be eaten by the sea monster Cetus...
. It is also known as the Andromeda GalaxyAndromeda GalaxyThe Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...
, and is readily visible to the naked eye in a modestly dark sky. - 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 31NGC 31NGC 31 is a spiral galaxy located in the Phoenix constellation....
, a spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation PhoenixPhoenix (constellation)Phoenix is a minor constellation in the southern sky. It is named after the Phoenix, a mythical bird. It is faint: there are only two stars in the whole constellation which are brighter than magnitude 5.0... - 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 -1805 January 31 and ended on -489 March 31. The duration of Saros series 31 was 1316.2 years, and it contained 74 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 -1774 May 30 and ended on -476 July 17. The duration of Saros series 31 was 1298.1 years, and it contained 73 lunar eclipses.
In sports
The jersey number 31 has been retired by several North American sportsMajor professional sports leagues of the United States and Canada
The major professional sports leagues, or simply major leagues, in the United States and Canada are the highest professional competitions in team sports...
teams in honor of past playing greats:
- 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 San Diego PadresSan Diego PadresThe San Diego Padres are a Major League Baseball team based in San Diego, California. They play in the National League Western Division. Founded in 1969, the Padres have won the National League Pennant twice, in 1984 and 1998, losing in the World Series both times...
, for Dave WinfieldDave WinfieldDavid Mark Winfield is an American former Major League Baseball outfielder. He is currently Executive Vice President/Senior Advisor of the San Diego Padres and an analyst for the ESPN program Baseball Tonight...
. - The Chicago CubsChicago CubsThe Chicago Cubs are a professional baseball team located in Chicago, Illinois. They are members of the Central Division of Major League Baseball's National League. They are one of two Major League clubs based in Chicago . The Cubs are also one of the two remaining charter members of the National...
, for Ferguson JenkinsFerguson JenkinsFerguson Arthur "Fergie" Jenkins, CM, is a Canadian former Major League Baseball right-handed pitcher. He was a three-time All-Star and the 1971 NL Cy Young Award winner. In 1991, Jenkins was inducted into the Baseball Hall of Fame. During a 19-year career, he pitched for four different teams,...
and Greg MadduxGreg MadduxGregory Alan Maddux , nicknamed "Mad Dog" and "The Professor", is a former Major League Baseball pitcher. He was the first pitcher in major league history to win the Cy Young Award for four consecutive years , a feat matched only by Randy Johnson...
. - The Atlanta BravesAtlanta BravesThe Atlanta Braves are a professional baseball club based in Atlanta, Georgia. The Braves are a member of the Eastern Division of Major League Baseball's National League. The Braves have played in Turner Field since 1997....
, also for Maddux.
- The San Diego Padres
- 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 Boston CelticsBoston CelticsThe Boston Celtics are a National Basketball Association team based in Boston, Massachusetts. They play in the Atlantic Division of the Eastern Conference. Founded in 1946, the team is currently owned by Boston Basketball Partners LLC. The Celtics play their home games at the TD Garden, which...
, for Cedric MaxwellCedric MaxwellCedric Bryan Maxwell is a retired American professional basketball player now in radio broadcasting. Nicknamed "Cornbread", he played 11 seasons in the NBA, and played a key role in two championships with the Boston Celtics.-College career:Maxwell was a star forward/center for the Charlotte 49ers...
. - The Indiana PacersIndiana PacersThe Indiana Pacers are a professional basketball team based in Indianapolis, Indiana. They are members of the Central Division of the Eastern Conference of the National Basketball Association...
, for Reggie MillerReggie MillerReginald Wayne "Reggie" Miller is a retired American professional basketball player who played his entire 18-year National Basketball Association career with the Indiana Pacers...
.
- The Boston Celtics
- In the NHLNational Hockey LeagueThe National Hockey League is an unincorporated not-for-profit association which operates a major professional ice hockey league of 30 franchised member clubs, of which 7 are currently located in Canada and 23 in the United States...
:- The Edmonton OilersEdmonton OilersThe Edmonton Oilers are a professional ice hockey team based in Edmonton, Alberta, Canada. They are members of the Northwest Division in the Western Conference of the National Hockey League ....
, for Grant FuhrGrant FuhrGrant Scott Fuhr is a Canadian former ice hockey goaltender in the National Hockey League and currently the goaltending coach for the Phoenix Coyotes. In 2003, he was inducted into the Hockey Hall of Fame...
. - The New York IslandersNew York IslandersThe New York Islanders are a professional ice hockey team based in Uniondale, New York. They are members of the Atlantic Division of the Eastern Conference of the National Hockey League...
, for Billy SmithBilly Smith (ice hockey)William John Smith, better known as Billy Smith, is a retired professional ice hockey goaltender and is best known for winning four Stanley Cups with the New York Islanders and being the first goalie to be credited with a goal....
.
- The Edmonton Oilers
- 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 Atlanta FalconsAtlanta FalconsThe Atlanta Falcons are a professional American football team based in Atlanta, Georgia. They are a member of the South Division of the National Football Conference in the National Football League...
, for William Andrews. - The New Orleans SaintsNew Orleans SaintsThe New Orleans Saints are a professional American football team based in New Orleans, Louisiana. They are members of the South Division of the National Football Conference of the National Football League ....
, for Jim Taylor.
- The Atlanta Falcons
[NASCAR]] driver Jeff Burton
Jeff Burton
Jeffrey Brian "Jeff" Burton , also referred to as JB or The Mayor, is a NASCAR Sprint Cup Series driver who drives the #31 Caterpillar Chevrolet Impala for Richard Childress Racing. Burton is the younger brother of Ward Burton, who is a former Sprint Cup driver...
drives #31, a car which was subject to a controversy when one of the sponsors changed its name after merging with another company.
In ice hockey
Ice hockey
Ice hockey, often referred to as hockey, is a team sport played on ice, in which skaters use wooden or composite sticks to shoot a hard rubber puck into their opponent's net. The game is played between two teams of six players each. Five members of each team skate up and down the ice trying to take...
goaltenders often wear the number 31.
In football the number 31 has been retired by Queens Park Rangers F.C.
Queens Park Rangers F.C.
Queens Park Rangers Football Club is an English professional football club, based in White City, Hammersmith and Fulham, west London. As the 2010-11 Football League Championship champions, they now play in the top tier of English football the Premier League, for the first time in 15 years...
in memory of Ray Jones (footballer born 1988)
In other fields
Thirty-one is also:- The number of musical triads (12 major, 12 minor, 4 diminished, and 3 augmented). (See triad (music)Triad (music)In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...
.) - The number of days in the months January, March, May, July, August, October and December
- The code for international direct-dial phone calls to the NetherlandsNetherlandsThe Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
- A card gameCard gameA card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games...
(see Thirty-one (game)Thirty-one (game)Thirty-one is a gambling card game played by two to seven people. The game is also known as Big Tonka, Blitz, "Clinker", "Klinker", "Skat", Cadillac in south Louisiana, Whammy! in central Indiana, and as Skedaddle, Snip Snap Snoop, Schnautz, Stop the Bus or Ride the Bus in other countries...
) - A type of game played on a backgammonBackgammonBackgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits...
board - The number of flavors of Baskin-RobbinsBaskin-RobbinsBaskin-Robbins is a global chain of ice cream parlors founded by Burt Baskin and Irvine Robbins in 1953, from the merging of their respective ice cream parlors, in Glendale, California. It claims to be the world's largest ice cream franchise, with more than 5,800 locations, 2,800 of which are...
ice creamIce creamIce cream is a frozen dessert usually made from dairy products, such as milk and cream, and often combined with fruits or other ingredients and flavours. Most varieties contain sugar, although some are made with other sweeteners...
and the shops are called 31 Ice Cream in JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south... - ISO 31ISO 31International Standard ISO 31 was the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide...
is the ISOInternational Organization for StandardizationThe International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...
's standard for quantities and units - In the title of the anime Ulysses 31Ulysses 31is a Franco-Japanese animated television series that updates the Greek mythology of Odysseus to the 31st century. The show comprised 26 half-hour episodes and was produced by DIC Audiovisuel in conjunction with anime studio Tokyo Movie Shinsha...
- In the title of Nick Hornby's book 31 Songs31 SongsSongbook is a 2002 collection of 26 essays by English writer Nick Hornby about songs and the particular emotional resonance they carry for him. In the UK, Sony released a stand-alone CD, A Selection of Music from 31 Songs, featuring 18 songs. The hardcover edition of Songbook, published in the U.S...
- Turkish slang for masturbationMasturbationMasturbation refers to sexual stimulation of a person's own genitals, usually to the point of orgasm. The stimulation can be performed manually, by use of objects or tools, or by some combination of these methods. Masturbation is a common form of autoeroticism...
("otuzbir") - A women's honorary at The University of Alabama (XXXI)
- The number of the French department Haute-GaronneHaute-GaronneHaute-Garonne is a department in the southwest of France named after the Garonne river. Its main city is Toulouse.-History:Haute-Garonne is one of the original 83 departments created during the French Revolution on March 4, 1790. It was created from part of the former province of Languedoc.The...
- In music, 31-tone equal temperament is a historically significant tuning system (31 equal temperament31 equal temperamentIn music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...
), first theorized by Christian Huygens and promulgated in the 20th century by Adriaan FokkerAdriaan FokkerAdriaan Daniël Fokker , was a Dutch physicist and musician.Fokker was born in Buitenzorg, Dutch East Indies ; he was a cousin of the aeronautical engineer Anthony Fokker...
External links
- Prime Curios! 31 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...