Examine individual changes

'{{other uses|17 (disambiguation)}} {{Infobox number | number = 17 | numeral = septendecimal | factorization = [[prime number|prime]] | prime = 7th | divisor = 1, 17 }} '''17''' ('''seventeen''') is the [[natural number]] following [[16 (number)|16]] and preceding [[18 (number)|18]]. It is a [[prime number]]. Seventeen is the sum of the first four prime numbers. == In mathematics == Seventeen is the seventh [[prime number]]. The next prime is [[19 (number)|nineteen]], with which it forms a [[twin prime]]. Seventeen is a [[permutable prime]] and a [[supersingular prime (moonshine theory)|supersingular prime]]. Seventeen is the third [[Fermat prime]], as it is of the form 2{{sup|2{{sup|''n''}}}} + 1, specifically with ''n'' = 2.<ref>{{Cite web|url=https://oeis.org/A019434|title=Sloane's A019434 : Fermat primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-01}}</ref> Since 17 is a Fermat prime, regular [[heptadecagon]]s can be [[constructible polygon|constructed]] with a [[compass]] and unmarked ruler. This was proven by [[Carl Friedrich Gauss]]<ref>John H. Conway and Richard K. Guy, ''The Book of Numbers''. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compasses."</ref> and ultimately led him to choose mathematics over philology for his studies.<ref>Pappas, Theoni, ''Mathematical Snippets'', 2008, p. 42.</ref> There are exactly 17 two-dimensional space (plane symmetry) [[group (mathematics)|groups]]. These are sometimes called [[wallpaper group]]s, as they represent the seventeen possible symmetry types that can be used for [[wallpaper]]. Like [[41 (number)|41]], the number 17 is a prime that yields primes in the [[polynomial]] ''n''²&nbsp;+&nbsp;''n''&nbsp;+&nbsp;''p'', for all positive ''n''&nbsp;<&nbsp;''p''&nbsp;&minus;&nbsp;1. Either 16 or 18 [[unit square]]s can be formed into rectangles with perimeter equal to the area; and there are no other [[natural number]]s with this property. The [[Platonist]]s regarded this as a sign of their peculiar propriety; and [[Plutarch]] notes it when writing that the [[Pythagoreans]] "utterly abominate" 17, which "bars them off from each other and disjoins them".<ref>{{Cite book|last=Babbitt|first=Frank Cole|title=Plutarch's Moralia|publisher=Loeb|year=1936|volume=V|url=https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html#42}}</ref> Seventeen is the minimum possible number of givens for a [[sudoku]] puzzle with a unique solution. This was long conjectured, and was proved in 2012–14.<ref>{{cite arxiv|last=McGuire|first=Gary|title=There is no 16-clue sudoku: solving the sudoku minimum number of clues problem|eprint=1201.0749|class=cs.DS|year=2012}}</ref><ref>{{Cite journal |last1=McGuire |first1=Gary |last2=Tugemann |first2=Bastian |last3=Civario |first3=Gilles |s2cid=8973439 |date=2014 |title=There is no 16-clue sudoku: Solving the sudoku minimum number of clues problem via hitting set enumeration |journal=Experimental Mathematics |volume=23 |issue=2 |pages=190–217 |doi=10.1080/10586458.2013.870056 }}</ref> There are 17 orthogonal curvilinear [[coordinate systems]] (to within a conformal symmetry) in which the three-variable [[Laplace equation]] can be solved using the [[separation of variables]] technique. Seventeen is the sixth [[Mersenne prime]] exponent, yielding 131071. Seventeen is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest ''n'' such that ''x''³ + ''y''² = ''n'' has two different solutions for ''x'' and ''y'' positive integers ((1,4) or (2,3)). The next such number is&nbsp;[[65 (number)|65]]. Seventeen is the minimum number of vertices on a graph such that, if the edges are coloured with three different colours, there is bound to be a monochromatic triangle. (See [[Ramsey's theorem#A multicolour example: R.283.2C3.2C3.29 .3D 17|Ramsey's theorem]].) Seventeen is the only prime number which is the sum of four consecutive primes (2,3,5,7). Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. The sequence of residues (mod ''n'') of a [[Googol#Properties|googol]] and [[Googolplex#Mod n|googolplex]], for ''n'' = 1, 2, 3, ..., agree up until ''n'' = 17. ==In science== * The [[atomic number]] of [[chlorine]]. * The [[Brodmann area]] defining the [[occipital lobe|primary visual processing area]] of mammalian brains. * [[Group (periodic table)|Group 17]] of the [[periodic table]] is called the [[halogens]]. * The number of elementary particles in the [[Standard Model]] of physics.<ref>{{cite web|url=http://physics.info/standard/|title=The Standard Model|author=Glenn Elert}}</ref> ==In languages== ===Grammar=== In Catalan, 17 is the first compound number (''disset''). The numbers 11 (''onze'') through 16 (''setze'') have their own names. In French, 17 is the first compound number (''dix-sept''). The numbers 11 (''onze'') through 16 (''seize'') have their own names. In Italian, 17 is also the first compound number (''diciassette''), whereas sixteen is ''sedici''. ==Age 17== * In most countries across the world, it is the last age at which one is considered a [[Minor (law)|minor]] under law. * In the UK, the minimum age for taking [[driver's education|driving lessons]], and to drive a car or a van * In the US and Canada, it is the age at which one may purchase, rent, or reserve [[Entertainment Software Rating Board#Restricted ratings|M-rated]] video games without parental consent * In some US states,<ref>{{cite web|url=http://www.age-of-consent.info/|archive-url=https://web.archive.org/web/20110417024317/http://www.age-of-consent.info/|url-status=dead|archive-date=2011-04-17|title=Age Of Consent By State}}</ref> and some jurisdictions around the world, 17 is the [[age of consent|age of sexual consent]]<ref>{{cite web|url=http://www.avert.org/age-of-consent.htm|title=Age of consent for sexual intercourse|date=2015-06-23}}</ref> * In most US states, Canada and in the UK, the age at which one may [[donate blood]] (without parental consent) * In many countries and jurisdictions, the age at which one may obtain a [[driver's license]] * In the US, the age at which one may watch, rent, or purchase [[Motion Picture Association of America film rating system|R-rated]] movies without parental consent *The U.S. [[TV Parental Guidelines]] system sets 17 as the minimum age one can watch programs with a TV-MA rating without parental guidance. * In the US, the age at which one can enlist in the armed forces with parental consent * In the US, the age at which one can apply for a [[private pilot licence]] for powered flight (however, applicants can obtain a student pilot certificate at age 16) * In Greece and Indonesia, the voting age * In Chile and Indonesia, the minimum driving age. ==In culture== ===Music=== {{main|17 (disambiguation)#Music}} ====Bands==== * [[17 Hippies]], a German band * [[Seventeen (South Korean band)|Seventeen]] (세븐틴), a South Korean boy band * [[Heaven 17]], an English new wave band * [[East 17]], an English boy band ====Albums==== * [[17 (XXXTentacion album)|''17'' (XXXTentacion album)]] * [[17 (Motel album)|''17'' (Motel album)]] * [[17 (Ricky Martin album)|''17'' (Ricky Martin album)]] * ''[[Chicago 17]]'', a 1984 album by Chicago * ''[[Seventeen Days]]'', a 2005 album by 3 Doors Down * ''[[Seventeen Seconds]]'', a 1980 album by The Cure * ''17 Carat'', a 2015 EP by [[Seventeen (South Korean band)|Seventeen]] ====Songs==== * [[17 (Sky Ferreira song)|"17" (Sky Ferreira song)]] * [[17 (Yourcodenameis:Milo song)|"17" (Yourcodenameis:Milo song)]] * "[[17 Again (song)|17 Again]]", a song by Eurythmics * "[[17 år]]", a song by Veronica Maggio * "17 Crimes", a song by [[AFI (band)|AFI]] * "[[17 Days (song)|17 Days]]", a song by Prince * "17", a song by [[Dan Bălan]] * "17", a song by [[Jethro Tull (band)|Jethro Tull]] * "17", a song by [[Kings of Leon]] * "17", a song by [[Milburn (band)|Milburn]] * "17", a song by Rick James from ''[[Reflections (Rick James album)|Reflections]]'' * "17", a B-side by [[Shiina Ringo]] on the "Tsumi to Batsu" single * "17", a song by [[The Smashing Pumpkins]] from the album ''[[Adore (The Smashing Pumpkins album)|Adore]]'' * "17", a song by [[Youth Lagoon]] from the album ''[[The Year of Hibernation]]'' * "17 Days", a song by [[Prince & the Revolution]], B side from the 1984 "When Doves Cry" single * [[Seventeen (Jet song)|"Seventeen" (Jet song)]] * [[Seventeen (Ladytron song)|"Seventeen" (Ladytron song)]] * [[Seventeen (Winger song)|"Seventeen" (Winger song)]] * "Seventeen", a song by ¡Forward, Russia! from ''[[Give Me a Wall]]'' * "Seventeen", a song by Jimmy Eat World from ''[[Static Prevails]]'' * "Seventeen", a song by Marina & the Diamonds from the US edition of ''[[The Family Jewels (Marina and the Diamonds album)|The Family Jewels]]'' * "Seventeen", a song by Mat Kearney from the iTunes edition of ''[[Young Love (Mat Kearney album)|Young Love]]'' * "Seventeen", a song from the [[Repo! The Genetic Opera (soundtrack)|''Repo! The Genetic Opera'' soundtrack]] * "Seventeen", the original title of the song "[[I Saw Her Standing There]]" by [[The Beatles]] * "Seventeen", a song by the [[Sex Pistols]] from ''[[Never Mind the Bollocks, Here's the Sex Pistols]]'' * "[[Seventeen Forever]]", a song by Metro Station * "[[At Seventeen]]", a song by Janis Ian * "[[Edge of Seventeen (song)|Edge of Seventeen]]", a song by Stevie Nicks * "Seventeen Ain't So Sweet", a song by The Red Jumpsuit Apparatus from ''[[Don't You Fake It]]'' * "Only 17", a song by [[Rucka Rucka Ali]] * "Opus 17 (Don't You Worry 'Bout Me)", a song by [[Frankie Valli and the Four Seasons]] * "(She's) Sexy + 17", a song by Stray Cats from ''[[Rant N' Rave with the Stray Cats]]'' * "Hello, Seventeen", a song by [[12012]] * "Section 17 (Suitcase Calling)", a song by [[The Polyphonic Spree]] * "Day Seventeen: Accident?", a song by [[Ayreon]] * "Seventeen", a song by [[Alessia Cara]] * "Seventeen", a song performed by [[Marina and the Diamonds]] * "Seventeen" and "Seventeen (Reprise)", songs in the musical ''[[Heathers: The Musical|Heathers]]'' * "Seventeen" and "Seventeen (Reprise)", songs in the musical ''[[Tuck Everlasting (musical)|Tuck Everlasting]]'' ====Other==== * [[Seventeen (musical)|''Seventeen'' (musical)]], a 1951 American musical * The ratio 18:17 was a popular approximation for the [[equal temperament|equal tempered]] [[semitone]] during the Renaissance poop ===Film=== * ''[[Seventeen (1916 film)|Seventeen]]'' (1916), an adaptation of the [[Seventeen (Tarkington novel)|novel of the same name]] by [[Booth Tarkington]] * ''[[Number 17 (1928 film)|Number 17]]'' (1928), a British-German film * ''[[Number Seventeen]]'' (1932), directed by [[Alfred Hitchcock]] * ''[[Seventeen (1940 film)|Seventeen]]'' (1940), a second adaptation of the Tarkington novel * ''[[Number 17 (1949 film)|Number 17]] (1949), a Swedish film * ''[[Stalag 17]]'' (1953), directed by [[Billy Wilder]] * ''[[All I Want (film)|Try Seventeen]]'' (2002), directed by Jeffrey Porter * In 2004, Volatile Films released a feature-length film titled ''The Significance of Seventeen'' starring [[Cindy Taylor]]; one theme addressed by the film is the high incidence of the number 17 and its function as 'the most random number' as described by [[MIT]]. * In the film ''[[Three Days of the Condor]]'', the title character played by [[Robert Redford]] works in section 17 of the [[CIA]]. *'' [[17 Again (film)|17 Again]]'' (2009), directed by [[Burr Steers]] ===Anime and manga=== * [[Android 17]], a character from the ''[[Dragon Ball]]'' series * Detective Konawaka from the [[Paprika (anime)|''Paprika'']] anime has a strong dislike for the number 17 ===Games=== * The computer game ''[[Half-Life 2]]'' takes place in and around [[City 17]] * The visual novel ''[[Ever 17: The Out of Infinity]]'' strongly revolves around the number 17 ===Print=== * The title of ''[[Seventeen (American magazine)|Seventeen]]'', a magazine * The title of ''[[Just Seventeen]]'', a former magazine * The number 17 is a recurring theme in the works of [[novelist]] [[Steven Brust]]. All of his chaptered novels have either 17 chapters or two books of 17 chapters each. Multiples of 17 frequently appear in his novels set in the fantasy world of [[Dragaera]], where the number is considered holy. * In ''[[The Illuminatus! Trilogy]]'', the symbol for [[Discordianism]] includes a pyramid with 17 steps because 17 has "virtually no interesting geometric, arithmetic, or mystical qualities". However, for the [[Illuminati]], 17 is tied with the "[[23 (numerology)|23/17 phenomenon]]". * In the [[Harry Potter universe]] ** 17 is the coming of age for wizards. It is equivalent to the usual coming of age at 18 ** 17 is the number of Sickles in one Galleon in the [[Harry Potter Universe#Coins|British wizards' currency]] ===Religion=== * According to [[Plutarch]]'s [[Moralia]], the Egyptians have a legend that the end of Osiris' life came on the seventeenth of a month, on which day it is quite evident to the eye that the period of the full moon is over. Now, because of this, the Pythagoreans call this day "the Barrier," and utterly abominate this number. For the number seventeen, coming in between the square sixteen and the oblong rectangle eighteen, which, as it happens, are the only plane figures that have their perimeters equal their areas, bars them off from each other and disjoins them, and breaks up the [[epogdoon]] by its division into unequal intervals.<ref>{{cite book|url=https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html|author=Plutarch, Moralia|title=Isis and Osiris (Part 3 of 5)|publisher= Loeb Classical Library edition|date=1936}}</ref> * In the [[Yasna]] of [[Zoroastrianism]], seventeen chapters were written by [[Zoroaster]] himself. These are the [[Gathas]]. * The number of the [[raka'ah]]s that Muslims perform during [[Salat]] on a daily basis. * The number of [[sura]]t [[al-Isra]] in the [[Qur'an]]. ==In sports== * 17 is the number of the longest winning streak in NHL history, which the [[Pittsburgh Penguins]] achieved in 1993. * [[Larry Ellison]]'s victorious 2013 [[Americas Cup]] Oracle racing yacht bears the name "17". * 17 is the number of the record for most NBA championships in NBA History, which the [[Boston Celtics]] (and as of 2020, the [[Los Angeles Lakers]]) achieved. ==In other fields== '''Seventeen''' is: * Described at [[MIT]] as 'the least random number', according to the [[Jargon File]].<ref>{{cite web|url=http://www.catb.org/~esr/jargon/html/R/random-numbers.html|title=random numbers|website=catb.org/}}</ref> This is supposedly because in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice. ** This study has been repeated a number of times.<ref>{{cite web|url=http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/|title=The Power of 17|work=Cosmic Variance}}</ref> * The number of guns in a 17-gun [[salute]] to U.S. Army, Air Force and Marine Corps Generals, and Navy and Coast Guard admirals. * The number of flames emanating from the grenade cap-badge of the [[Grenadier Guards]]. * During World War II, the four-engined heavy bomber as flown by the USAAF and other Allies and known as "The [[Flying Fortress]]", was also known as the B-17 * The maximum number of strokes of a [[radical (Chinese character)|Chinese radical]] * The number of syllables in a [[haiku]] (5 + 7 + 5) * In the [[Nordic countries]] the seventeenth day of the year is considered the ''heart'' and/or the ''back'' of winter * "Highway 17" or "Route 17": See [[List of highways numbered 17]] and [[List of public transport routes numbered 17]] * Seventeen, also known as Lock Seventeen, an unincorporated place in [[Clay Township, Tuscarawas County, Ohio]] * ''Seventeen'' was the former name of a yacht prior to being commissioned in the [[US Navy]] as the {{USS|Carnelian|PY-19}} [[Image:Alitalia-17.jpg|thumb|No row 17 in [[Alitalia]] planes]] * In [[Italian culture]], the number 17 is considered unlucky. When viewed as the Roman numeral, XVII, it is then changed anagrammatically to VIXI, which in the [[Latin language]] translates to "I lived", the [[perfect (grammar)|perfect]] implying "My life is over." (c.f. "''Vixerunt''", [[Cicero]]'s famous announcement of an execution.) [[Renault]] sold its "[[Renault 15/17|R17]]" model in Italy as "R177." See [[Cesana Pariol]] in the sport section about the name of curve 17. * The fear of the number 17 is called 'heptadecaphobia' or 'heptakaidekaphobia' * Some species of [[cicada]]s have a life cycle of 17 years (i.e. they are buried in the ground for 17 years between every mating season) * The number of special significance to [[Yellow Pig's Day]] and [[Hampshire College Summer Studies in Mathematics]] * The number to call police in France * [[Force 17]], a special operations unit of the Palestinian Fatah movement * The number of the French department [[Charente-Maritime]] * The declared percentage alcohol content (by volume) of Baileys Irish Cream - an Irish whiskey and cream based liqueur, made by Gilbeys of Ireland * The flight number of [[Malaysia Airlines Flight 17]] which was shot down on 17 July 2014 * The record number of [[concerts]] performed in a single year at [[Madison Square Garden]] by the band [[Phish]] in 2017<ref>{{cite news|url=https://www.nytimes.com/2017/08/07/arts/music/phish-bakers-dozen.html|title=Why Would You Go to a Phish Concert, Let Alone 13? I Found Out|first=Ben|last=Ratliff|date=7 August 2017|access-date=30 April 2018|newspaper=The New York Times}}</ref><ref>{{cite web|url=https://livemusicblog.com/2017/12/27/phish-new-years-eve/|title=Phish Returns to Madison Square Garden for New Year's Eve; Here's What We Think Will Go Down (Hint: Cosmic Wristbands) - LIVE music blog|date=27 December 2017|website=livemusicblog.com|access-date=30 April 2018}}</ref> * The number of deaths and injured people on February 14, 2018, shooting at the Marjory [[Stoneman Douglas High School shooting]]. ==References== <references/> *{{cite journal|author1=Berlekamp, E. R. |author2-link=Ronald L. Graham |author2=Graham, R. L. |title=Irregularities in the distributions of finite sequences | journal = [[Journal of Number Theory]]|volume=2|year=1970|pages=152–161|mr=0269605|doi=10.1016/0022-314X(70)90015-6|issue=2|bibcode=1970JNT.....2..152B|author1-link=Elwyn Berlekamp |doi-access=free}} ==External links== {{Commons category}} {{wiktionary|seventeen}} * [http://www.vinc17.org/d17_eng.html Properties of 17] * [http://www.yellowpigs.net/index.php?topic=yellowpigs/YP_seventeen Mathematical properties of 17] {{Webarchive|url=https://web.archive.org/web/20190729010229/https://www.yellowpigs.net/index.php?topic=yellowpigs%2FYP_seventeen |date=2019-07-29 }} at yellowpigs.net * [https://web.archive.org/web/20100705142954/http://www.hilmar-alquiros.de/siebzehn.htm 17] * [https://web.archive.org/web/20110818122755/http://scienceblogs.com/cognitivedaily/2007/02/is_17_the_most_random_number.php is 17 the most random number] at the wayback machine. *[https://www.VirtueScience.com/17.html Number 17 at the Database of Number Correlations] *[https://primes.utm.edu/curios/page.php/17.html Prime Curios for the number 17] {{Integers|zero}} {{DEFAULTSORT:17 (Number)}} [[Category:Integers]]'