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VariableValue
Edit count of the user (user_editcount)
7
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Page title without namespace (page_title)
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'{{other uses|17 (disambiguation){{!}}17}} {{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]], which makes it the fourth [[super-prime]],<ref>{{Cite OEIS |A006450 |Prime-indexed primes: primes with prime subscripts. |access-date=2023-06-29 }}</ref> as [[7|seven]] is itself prime. It forms a [[twin prime]] with [[19 (number)|19]],<ref>{{Cite OEIS |A001359 |Lesser of twin primes |access-date=2022-11-25 }}</ref> a [[cousin prime]] with [[13 (number)|13]],<ref>{{Cite OEIS |A046132 |Larger member p+4 of cousin primes |access-date=2022-11-25 }}</ref> and a [[sexy prime]] with both [[11 (number)|11]] and [[23 (number)|23]].<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes) |access-date=2022-11-25 }}</ref> Seventeen is the only prime number which is the sum of ''four'' consecutive primes ([[2]], [[3]], [[5]], and [[7]]), as any other four consecutive primes that are added always generate an even number divisible by two. It is one of six [[lucky numbers of Euler]] which produce primes of the form <math>k^{2}-k+41</math>,<ref>{{Cite OEIS |A014556 |Euler's "Lucky" numbers |access-date=2022-11-25 }}</ref> and the sixth [[Mersenne prime]] exponent, which yields 131,071.<ref>{{Cite OEIS |A000043 |Mersenne exponents |access-date=2022-11-25 }}</ref> It is also the minimum possible number of givens for a [[sudoku]] puzzle with a unique solution.<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> 17 can be written in the form <math>x^y + y^x</math> and <math>x^y - y^x</math>; and as such, it is a [[Leyland number#Leyland primes|Leyland prime]] and [[Leyland number#Leyland number of the second kind|Leyland prime of the second kind]]:<ref>{{Cite OEIS |A094133 |Leyland primes |access-date=2022-11-25 }}</ref><ref>{{Cite OEIS |A045575 |Leyland primes of the second kind |access-date=2022-11-25 }}</ref> :<math>2^{3} + 3^{2} = 17 = 3^{4} - 4^{3}</math> 17 is the third [[Fermat prime]], as it is of the form <math>2^{2^{n}} + 1</math> with <math>n = 2</math>.<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> On the other hand, the seventeenth [[Jacobsthal number|Jacobsthal–Lucas number]] — that is part of a [[sequence]] which includes four Fermat primes (except for [[3]]) — is the fifth and largest known Fermat prime: [[65,537]].<ref>{{Cite OEIS |A014551 |Jacobsthal-Lucas numbers. |access-date=2023-06-29 }}</ref> It is one more than the smallest number with exactly seventeen [[divisor]]s, [[65,536 (number)|65,536]] = 2<sup>16</sup>.<ref>{{Cite OEIS |A005179 |Smallest number with exactly n divisors. |access-date=2023-06-28 }}</ref> Since seventeen 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]] and ultimately led him to choose mathematics over philology for his studies.<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><ref>[[Theoni Pappas|Pappas, Theoni]], ''Mathematical Snippets'', 2008, p. 42.</ref> 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> 17 is the minimum number of [[Vertex (geometry)|vertices]] on a [[Graph (discrete mathematics)|graph]] such that, if the [[Edge (geometry)|edges]] are colored with three different colors, 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]].<ref>{{Cite OEIS |A003323 |Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's. |access-date=2022-11-25 }}</ref> There are also: * 17 [[Space group#Classification systems|crystallographic space groups]] in two dimensions.<ref>{{Cite OEIS |A006227 |Number of n-dimensional space groups (including enantiomorphs) |access-date=2022-11-25 }}</ref> These are sometimes called [[wallpaper group]]s, as they represent the seventeen possible symmetry types that can be used for [[wallpaper]]. * 17 combinations of regular polygons that completely [[Vertex (geometry)#Of a plane tiling|fill a plane vertex]].<ref>{{citation|title=The Elements of Plane Practical Geometry, Etc|first=Elmslie William|last=Dallas|publisher=John W. Parker & Son|year=1855|page=134|url=https://books.google.com/books?id=y4BaAAAAcAAJ&pg=PA134}}.</ref> Eleven of these belong to [[Euclidean tilings of convex regular polygons#Regular tilings|regular and semiregular tilings]], while 6 of these (3.7.42,<ref>{{Cite web|url=http://gruze.org/tilings/3_7_42_shield|title=Shield - a 3.7.42 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Icositetragon#Related polygons|3.8.24]],<ref>{{Cite web|url=http://gruze.org/tilings/dancer|title=Dancer - a 3.8.24 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Octadecagon#Uses|3.9.18]],<ref>{{Cite web|url=http://gruze.org/tilings/3_9_18_art|title=Art - a 3.9.18 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Pentadecagon#Uses|3.10.15]],<ref>{{Cite web|url=http://gruze.org/tilings/3_10_15_fighters|title=Fighters - a 3.10.15 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Icosagon#Uses|4.5.20]],<ref>{{Cite web|url=http://gruze.org/tilings/compass|title=Compass - a 4.5.20 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> and 5.5.10)<ref>{{Cite web|url=http://gruze.org/tilings/5_5_10_broken_roses|title=Broken roses - three 5.5.10 tilings|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> exclusively surround a point in the plane and fill it only when irregular polygons are included.<ref>{{Cite web|url=https://blogs.ams.org/visualinsight/2015/02/01/pentagon-decagon-packing/|title=Pentagon-Decagon Packing|website=American Mathematical Society|publisher=AMS|access-date=2022-03-07}}</ref> * 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. * 17 distinct [[Stellation#Stellating polyhedra|fully supported stellations]] generated by an [[Regular icosahedron|icosahedron]].<ref name="Stellations">{{Cite web |url=https://www.software3d.com/Enumerate.php |last=Webb |first=Robert |title=Enumeration of Stellations |website=www.software3d.com |access-date=2022-11-25 |archive-url=http://archive.today/2022.11.26-015207/https://www.software3d.com/Enumerate.php |archive-date=2022-11-25 }}</ref> The seventeenth prime number is [[59 (number)|59]], which is equal to the total number of stellations of the icosahedron by [[Stellation#Miller's rules|Miller's rules]].<ref>{{Cite book |author1=[[Coxeter|H. S. M. Coxeter]] |author2=P. Du Val |author3=H. T. Flather |author4=J. F. Petrie |title=The Fifty-Nine Icosahedra |publisher=Springer |location=New York |year=1982 |doi=10.1007/978-1-4613-8216-4 |isbn=978-1-4613-8216-4 }}</ref><ref>{{Cite OEIS |A000040 |The prime numbers |access-date=2023-02-17 }}</ref> Without counting the icosahedron as a ''zeroth'' stellation, this total becomes [[58 (number)|58]], a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17).<ref>{{Cite OEIS|A007504 |Sum of the first n primes. |access-date=2023-02-17 }}</ref> :17 distinct fully supported stellations are also produced by [[truncated cube]] and [[truncated octahedron]].<ref name="Stellations"/> * 17 four-dimensional [[Parallelohedron|parallelotopes]] that are [[Zonohedron#Zonotopes|zonotopes]]. Another 34, or twice 17, are [[Minkowski sum]]s of zonotopes with the [[24-cell]], itself the simplest parallelotope that is not a zonotope.<ref>{{cite journal|last1=Senechal|first1=Marjorie|author1-link=Marjorie Senechal|last2=Galiulin|first2=R. V.|hdl=2099/1195|issue=10|journal=Structural Topology|language=en,fr|mr=768703|pages=5–22|title=An introduction to the theory of figures: the geometry of E. S. Fedorov|year=1984}}</ref> Seventeen is the highest dimension for [[Coxeter-Dynkin diagram#Hypercompact Coxeter groups (Vinberg polytopes)|paracompact Vineberg polytopes]] with rank <math>n+2</math> mirror [[Facet (geometry)|facets]], with the lowest belonging to the third.<ref>{{cite journal |last=Tumarkin |first=P.V. |date=May 2004 |title=Hyperbolic Coxeter N-Polytopes with n+2 Facets |journal=Mathematical Notes |url=https://doi.org/10.1023/B:MATN.0000030993.74338.dd |volume=75 |issue=5/6 |pages=848–854 |doi=10.1023/B:MATN.0000030993.74338.dd |arxiv=math/0301133 |access-date=18 March 2022}}</ref> The sequence of residues (mod {{mvar|n}}) of a [[Googol#Properties|googol]] and [[Googolplex#Mod n|googolplex]], for <math>n=1, 2, 3, ...</math>, agree up until <math>n=17</math>. In [[abstract algebra]], 17 is the seventh ''[[Supersingular prime (moonshine theory)|supersingular prime]]'' that divides the [[Order (group theory)|order]] of six [[sporadic group]]s ([[Janko group J3|''J<sub>3</sub>'']], [[Held group|''He'']], [[Fischer group Fi23|''Fi<sub>23</sub>'']], [[Fischer group Fi24|''Fi<sub>24</sub>]], [[Baby monster group|''B'']], and [[Monster group|''F<sub>1</sub>'']]) inside the [[Sporadic group#Happy Family|Happy Family]] of such groups.<ref>{{Cite OEIS |A002267 |The 15 supersingular primes |access-date=2022-11-25 }}</ref> The 16th and 18th prime numbers ([[53 (number)|53]] and [[61 (number)|61]]) are the only two primes less than [[71 (number)|71]] that do not divide the [[Order (group theory)|order]] of any sporadic group including the [[Pariah group|pariahs]], with this prime as the largest such supersingular prime that divides the largest of these groups (''F<sub>1</sub>''). On the other hand, if the [[Tits group]] is included as a ''non-strict'' group of [[Group of Lie type|Lie type]], then there are seventeen total classes of Lie groups that are simultaneously [[Finite group|finite]] and [[Simple group|simple]] (see, [[classification of finite simple groups]]). In [[base ten]], (17, 71) form the seventh permutation class of [[permutable prime]]s.<ref>{{Cite OEIS |A258706 |Absolute primes: every permutation of digits is a prime. Only the smallest representative of each permutation class is shown. |access-date=2023-06-29 }}</ref> A positive [[Definite quadratic form|definite quadratic]] [[integer matrix]] represents all [[prime number|primes]] when it contains at least the set of seventeen numbers: {2, 3, 5, 7, 11, 13, ''17'', 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}; only four prime numbers less than the largest member are not part of the set (53, [[59 (number)|59]], 61, and 71).<ref>{{Cite OEIS |A154363 |Numbers from Bhargava's prime-universality criterion theorem }}</ref> ==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 with unique names in the [[Standard Model]] of physics.<ref>{{cite journal|url=http://physics.info/standard/|title=The Standard Model|author=Glenn Elert|journal=The Physics Hypertextbook|year=2021}}</ref> ==In languages== ===Grammar=== In Catalan, 17 is the first compound number ({{lang|ca|disset}}). The numbers 11 ({{lang|ca|onze}}) through 16 ({{lang|ca|setze}}) have their own names. In French, 17 is the first compound number ({{lang|fr|dix-sept}}). The numbers 11 ({{lang|fr|onze}}) through 16 ({{lang|fr|seize}}) have their own names. In Italian, 17 is also the first compound number ({{lang|it|diciassette}}), whereas sixteen is {{lang|it|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 [[Tajikistan]], [[North Korea]] and [[Timor-Leste]], the [[age of majority]] ==In culture== ===Music=== {{main|17 (disambiguation)#Music}} ====Bands==== * [[17 Hippies]], a German band * [[Seventeen (South Korean band)|Seventeen]] ({{Lang|ko|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]] * ''Sector 17'', a 2022 repackaged album by [[Seventeen (South Korean band)|Seventeen]] ====Songs==== * "17 Again", a song by [[Tide Lines]] * [[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]]", 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'']], a 1951 American musical * The ratio 18:17 was a popular approximation for the [[equal temperament|equal tempered]] [[semitone]] during the Renaissance ===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 *'' [[17 Again (film)|17 Again]]'' (2009), directed by [[Burr Steers]] *The most popular skibidi toilet video was 17 ===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. * 17 is the number of individual laws mentioned in the [[Laws of the Game (association football)]]. * 17 is the number of games played by each [[NFL]] team as of 2021. * Since the start of the [[2014 Formula One World Championship|2014 season]], [[Formula One]] [[List of Formula One drivers|drivers]] have been able to choose [[List of Formula One driver numbers|their own car number]]; however, following the fatal accident of [[Jules Bianchi]], who drove car #17, the number was retired. ==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|access-date=2010-06-14|archive-date=2008-12-04|archive-url=https://web.archive.org/web/20081204111153/http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/|url-status=dead}}</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 maximum number of strokes of a [[radical (Chinese character)|Chinese radical]]. * The total 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 to call police in France. * [[Force 17]], a special operations unit of the Palestinian Fatah movement. * The number of the French department [[Charente-Maritime]]. * [[Malaysia Airlines Flight 17]] was [[List of aircraft shootdowns|shot down]] by Russian-controlled forces on 17 July 2014 after flying over eastern Ukraine. The first test flight of the plane, a [[Boeing 777-200ER]], was on 17 July 1997, exactly 17 years prior to the doomed flight. ==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]]'
New page wikitext, after the edit (new_wikitext)
' 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> 17 is the minimum number of [[Vertex (geometry)|vertices]] on a [[Graph (discrete mathematics)|graph]] such that, if the [[Edge (geometry)|edges]] are colored with three different colors, 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]].<ref>{{Cite OEIS |A003323 |Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's. |access-date=2022-11-25 }}</ref> There are also: * 17 [[Space group#Classification systems|crystallographic space groups]] in two dimensions.<ref>{{Cite OEIS |A006227 |Number of n-dimensional space groups (including enantiomorphs) |access-date=2022-11-25 }}</ref> These are sometimes called [[wallpaper group]]s, as they represent the seventeen possible symmetry types that can be used for [[wallpaper]]. * 17 combinations of regular polygons that completely [[Vertex (geometry)#Of a plane tiling|fill a plane vertex]].<ref>{{citation|title=The Elements of Plane Practical Geometry, Etc|first=Elmslie William|last=Dallas|publisher=John W. Parker & Son|year=1855|page=134|url=https://books.google.com/books?id=y4BaAAAAcAAJ&pg=PA134}}.</ref> Eleven of these belong to [[Euclidean tilings of convex regular polygons#Regular tilings|regular and semiregular tilings]], while 6 of these (3.7.42,<ref>{{Cite web|url=http://gruze.org/tilings/3_7_42_shield|title=Shield - a 3.7.42 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Icositetragon#Related polygons|3.8.24]],<ref>{{Cite web|url=http://gruze.org/tilings/dancer|title=Dancer - a 3.8.24 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Octadecagon#Uses|3.9.18]],<ref>{{Cite web|url=http://gruze.org/tilings/3_9_18_art|title=Art - a 3.9.18 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Pentadecagon#Uses|3.10.15]],<ref>{{Cite web|url=http://gruze.org/tilings/3_10_15_fighters|title=Fighters - a 3.10.15 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> [[Icosagon#Uses|4.5.20]],<ref>{{Cite web|url=http://gruze.org/tilings/compass|title=Compass - a 4.5.20 tiling|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> and 5.5.10)<ref>{{Cite web|url=http://gruze.org/tilings/5_5_10_broken_roses|title=Broken roses - three 5.5.10 tilings|website=Kevin Jardine's projects|publisher=Kevin Jardine|access-date=2022-03-07}}</ref> exclusively surround a point in the plane and fill it only when irregular polygons are included.<ref>{{Cite web|url=https://blogs.ams.org/visualinsight/2015/02/01/pentagon-decagon-packing/|title=Pentagon-Decagon Packing|website=American Mathematical Society|publisher=AMS|access-date=2022-03-07}}</ref> * 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. * 17 distinct [[Stellation#Stellating polyhedra|fully supported stellations]] generated by an [[Regular icosahedron|icosahedron]].<ref name="Stellations">{{Cite web |url=https://www.software3d.com/Enumerate.php |last=Webb |first=Robert |title=Enumeration of Stellations |website=www.software3d.com |access-date=2022-11-25 |archive-url=http://archive.today/2022.11.26-015207/https://www.software3d.com/Enumerate.php |archive-date=2022-11-25 }}</ref> The seventeenth prime number is [[59 (number)|59]], which is equal to the total number of stellations of the icosahedron by [[Stellation#Miller's rules|Miller's rules]].<ref>{{Cite book |author1=[[Coxeter|H. S. M. Coxeter]] |author2=P. Du Val |author3=H. T. Flather |author4=J. F. Petrie |title=The Fifty-Nine Icosahedra |publisher=Springer |location=New York |year=1982 |doi=10.1007/978-1-4613-8216-4 |isbn=978-1-4613-8216-4 }}</ref><ref>{{Cite OEIS |A000040 |The prime numbers |access-date=2023-02-17 }}</ref> Without counting the icosahedron as a ''zeroth'' stellation, this total becomes [[58 (number)|58]], a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17).<ref>{{Cite OEIS|A007504 |Sum of the first n primes. |access-date=2023-02-17 }}</ref> :17 distinct fully supported stellations are also produced by [[truncated cube]] and [[truncated octahedron]].<ref name="Stellations"/> * 17 four-dimensional [[Parallelohedron|parallelotopes]] that are [[Zonohedron#Zonotopes|zonotopes]]. Another 34, or twice 17, are [[Minkowski sum]]s of zonotopes with the [[24-cell]], itself the simplest parallelotope that is not a zonotope.<ref>{{cite journal|last1=Senechal|first1=Marjorie|author1-link=Marjorie Senechal|last2=Galiulin|first2=R. V.|hdl=2099/1195|issue=10|journal=Structural Topology|language=en,fr|mr=768703|pages=5–22|title=An introduction to the theory of figures: the geometry of E. S. Fedorov|year=1984}}</ref> Seventeen is the highest dimension for [[Coxeter-Dynkin diagram#Hypercompact Coxeter groups (Vinberg polytopes)|paracompact Vineberg polytopes]] with rank <math>n+2</math> mirror [[Facet (geometry)|facets]], with the lowest belonging to the third.<ref>{{cite journal |last=Tumarkin |first=P.V. |date=May 2004 |title=Hyperbolic Coxeter N-Polytopes with n+2 Facets |journal=Mathematical Notes |url=https://doi.org/10.1023/B:MATN.0000030993.74338.dd |volume=75 |issue=5/6 |pages=848–854 |doi=10.1023/B:MATN.0000030993.74338.dd |arxiv=math/0301133 |access-date=18 March 2022}}</ref> The sequence of residues (mod {{mvar|n}}) of a [[Googol#Properties|googol]] and [[Googolplex#Mod n|googolplex]], for <math>n=1, 2, 3, ...</math>, agree up until <math>n=17</math>. In [[abstract algebra]], 17 is the seventh ''[[Supersingular prime (moonshine theory)|supersingular prime]]'' that divides the [[Order (group theory)|order]] of six [[sporadic group]]s ([[Janko group J3|''J<sub>3</sub>'']], [[Held group|''He'']], [[Fischer group Fi23|''Fi<sub>23</sub>'']], [[Fischer group Fi24|''Fi<sub>24</sub>]], [[Baby monster group|''B'']], and [[Monster group|''F<sub>1</sub>'']]) inside the [[Sporadic group#Happy Family|Happy Family]] of such groups.<ref>{{Cite OEIS |A002267 |The 15 supersingular primes |access-date=2022-11-25 }}</ref> The 16th and 18th prime numbers ([[53 (number)|53]] and [[61 (number)|61]]) are the only two primes less than [[71 (number)|71]] that do not divide the [[Order (group theory)|order]] of any sporadic group including the [[Pariah group|pariahs]], with this prime as the largest such supersingular prime that divides the largest of these groups (''F<sub>1</sub>''). On the other hand, if the [[Tits group]] is included as a ''non-strict'' group of [[Group of Lie type|Lie type]], then there are seventeen total classes of Lie groups that are simultaneously [[Finite group|finite]] and [[Simple group|simple]] (see, [[classification of finite simple groups]]). In [[base ten]], (17, 71) form the seventh permutation class of [[permutable prime]]s.<ref>{{Cite OEIS |A258706 |Absolute primes: every permutation of digits is a prime. Only the smallest representative of each permutation class is shown. |access-date=2023-06-29 }}</ref> A positive [[Definite quadratic form|definite quadratic]] [[integer matrix]] represents all [[prime number|primes]] when it contains at least the set of seventeen numbers: {2, 3, 5, 7, 11, 13, ''17'', 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}; only four prime numbers less than the largest member are not part of the set (53, [[59 (number)|59]], 61, and 71).<ref>{{Cite OEIS |A154363 |Numbers from Bhargava's prime-universality criterion theorem }}</ref> ==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 with unique names in the [[Standard Model]] of physics.<ref>{{cite journal|url=http://physics.info/standard/|title=The Standard Model|author=Glenn Elert|journal=The Physics Hypertextbook|year=2021}}</ref> ==In languages== ===Grammar=== In Catalan, 17 is the first compound number ({{lang|ca|disset}}). The numbers 11 ({{lang|ca|onze}}) through 16 ({{lang|ca|setze}}) have their own names. In French, 17 is the first compound number ({{lang|fr|dix-sept}}). The numbers 11 ({{lang|fr|onze}}) through 16 ({{lang|fr|seize}}) have their own names. In Italian, 17 is also the first compound number ({{lang|it|diciassette}}), whereas sixteen is {{lang|it|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 [[Tajikistan]], [[North Korea]] and [[Timor-Leste]], the [[age of majority]] ==In culture== ===Music=== {{main|17 (disambiguation)#Music}} ====Bands==== * [[17 Hippies]], a German band * [[Seventeen (South Korean band)|Seventeen]] ({{Lang|ko|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]] * ''Sector 17'', a 2022 repackaged album by [[Seventeen (South Korean band)|Seventeen]] ====Songs==== * "17 Again", a song by [[Tide Lines]] * [[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]]", 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'']], a 1951 American musical * The ratio 18:17 was a popular approximation for the [[equal temperament|equal tempered]] [[semitone]] during the Renaissance ===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 *'' [[17 Again (film)|17 Again]]'' (2009), directed by [[Burr Steers]] *The most popular skibidi toilet video was 17 ===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. * 17 is the number of individual laws mentioned in the [[Laws of the Game (association football)]]. * 17 is the number of games played by each [[NFL]] team as of 2021. * Since the start of the [[2014 Formula One World Championship|2014 season]], [[Formula One]] [[List of Formula One drivers|drivers]] have been able to choose [[List of Formula One driver numbers|their own car number]]; however, following the fatal accident of [[Jules Bianchi]], who drove car #17, the number was retired. ==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|access-date=2010-06-14|archive-date=2008-12-04|archive-url=https://web.archive.org/web/20081204111153/http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/|url-status=dead}}</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 maximum number of strokes of a [[radical (Chinese character)|Chinese radical]]. * The total 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 to call police in France. * [[Force 17]], a special operations unit of the Palestinian Fatah movement. * The number of the French department [[Charente-Maritime]]. * [[Malaysia Airlines Flight 17]] was [[List of aircraft shootdowns|shot down]] by Russian-controlled forces on 17 July 2014 after flying over eastern Ukraine. The first test flight of the plane, a [[Boeing 777-200ER]], was on 17 July 1997, exactly 17 years prior to the doomed flight. ==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]]'
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'@@ -1,19 +1,3 @@ -{{other uses|17 (disambiguation){{!}}17}} -{{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]], which makes it the fourth [[super-prime]],<ref>{{Cite OEIS |A006450 |Prime-indexed primes: primes with prime subscripts. |access-date=2023-06-29 }}</ref> as [[7|seven]] is itself prime. It forms a [[twin prime]] with [[19 (number)|19]],<ref>{{Cite OEIS |A001359 |Lesser of twin primes |access-date=2022-11-25 }}</ref> a [[cousin prime]] with [[13 (number)|13]],<ref>{{Cite OEIS |A046132 |Larger member p+4 of cousin primes |access-date=2022-11-25 }}</ref> and a [[sexy prime]] with both [[11 (number)|11]] and [[23 (number)|23]].<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes) |access-date=2022-11-25 }}</ref> Seventeen is the only prime number which is the sum of ''four'' consecutive primes ([[2]], [[3]], [[5]], and [[7]]), as any other four consecutive primes that are added always generate an even number divisible by two. It is one of six [[lucky numbers of Euler]] which produce primes of the form <math>k^{2}-k+41</math>,<ref>{{Cite OEIS |A014556 |Euler's "Lucky" numbers |access-date=2022-11-25 }}</ref> and the sixth [[Mersenne prime]] exponent, which yields 131,071.<ref>{{Cite OEIS |A000043 |Mersenne exponents |access-date=2022-11-25 }}</ref> It is also the minimum possible number of givens for a [[sudoku]] puzzle with a unique solution.<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> 17 can be written in the form <math>x^y + y^x</math> and <math>x^y - y^x</math>; and as such, it is a [[Leyland number#Leyland primes|Leyland prime]] and [[Leyland number#Leyland number of the second kind|Leyland prime of the second kind]]:<ref>{{Cite OEIS |A094133 |Leyland primes |access-date=2022-11-25 }}</ref><ref>{{Cite OEIS |A045575 |Leyland primes of the second kind |access-date=2022-11-25 }}</ref> -:<math>2^{3} + 3^{2} = 17 = 3^{4} - 4^{3}</math> - -17 is the third [[Fermat prime]], as it is of the form <math>2^{2^{n}} + 1</math> with <math>n = 2</math>.<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> On the other hand, the seventeenth [[Jacobsthal number|Jacobsthal–Lucas number]] — that is part of a [[sequence]] which includes four Fermat primes (except for [[3]]) — is the fifth and largest known Fermat prime: [[65,537]].<ref>{{Cite OEIS |A014551 |Jacobsthal-Lucas numbers. |access-date=2023-06-29 }}</ref> It is one more than the smallest number with exactly seventeen [[divisor]]s, [[65,536 (number)|65,536]] = 2<sup>16</sup>.<ref>{{Cite OEIS |A005179 |Smallest number with exactly n divisors. |access-date=2023-06-28 }}</ref> Since seventeen 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]] and ultimately led him to choose mathematics over philology for his studies.<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><ref>[[Theoni Pappas|Pappas, Theoni]], ''Mathematical Snippets'', 2008, p. 42.</ref> 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> '
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[ 0 => '{{other uses|17 (disambiguation){{!}}17}}', 1 => '{{Infobox number', 2 => '| number = 17', 3 => '| numeral = septendecimal', 4 => '| factorization = [[prime number|prime]]', 5 => '| prime = 7th', 6 => '| divisor = 1, 17', 7 => '}}', 8 => ''''17''' ('''seventeen''') is the [[natural number]] following [[16 (number)|16]] and preceding [[18 (number)|18]]. It is a [[prime number]].', 9 => 'Seventeen is the sum of the first four prime numbers.', 10 => '', 11 => '== In mathematics ==', 12 => ''''Seventeen''' is the seventh [[prime number]], which makes it the fourth [[super-prime]],<ref>{{Cite OEIS |A006450 |Prime-indexed primes: primes with prime subscripts. |access-date=2023-06-29 }}</ref> as [[7|seven]] is itself prime. It forms a [[twin prime]] with [[19 (number)|19]],<ref>{{Cite OEIS |A001359 |Lesser of twin primes |access-date=2022-11-25 }}</ref> a [[cousin prime]] with [[13 (number)|13]],<ref>{{Cite OEIS |A046132 |Larger member p+4 of cousin primes |access-date=2022-11-25 }}</ref> and a [[sexy prime]] with both [[11 (number)|11]] and [[23 (number)|23]].<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes) |access-date=2022-11-25 }}</ref> Seventeen is the only prime number which is the sum of ''four'' consecutive primes ([[2]], [[3]], [[5]], and [[7]]), as any other four consecutive primes that are added always generate an even number divisible by two. It is one of six [[lucky numbers of Euler]] which produce primes of the form <math>k^{2}-k+41</math>,<ref>{{Cite OEIS |A014556 |Euler's "Lucky" numbers |access-date=2022-11-25 }}</ref> and the sixth [[Mersenne prime]] exponent, which yields 131,071.<ref>{{Cite OEIS |A000043 |Mersenne exponents |access-date=2022-11-25 }}</ref> It is also the minimum possible number of givens for a [[sudoku]] puzzle with a unique solution.<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> 17 can be written in the form <math>x^y + y^x</math> and <math>x^y - y^x</math>; and as such, it is a [[Leyland number#Leyland primes|Leyland prime]] and [[Leyland number#Leyland number of the second kind|Leyland prime of the second kind]]:<ref>{{Cite OEIS |A094133 |Leyland primes |access-date=2022-11-25 }}</ref><ref>{{Cite OEIS |A045575 |Leyland primes of the second kind |access-date=2022-11-25 }}</ref>', 13 => ':<math>2^{3} + 3^{2} = 17 = 3^{4} - 4^{3}</math>', 14 => '', 15 => '17 is the third [[Fermat prime]], as it is of the form <math>2^{2^{n}} + 1</math> with <math>n = 2</math>.<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> On the other hand, the seventeenth [[Jacobsthal number|Jacobsthal–Lucas number]] — that is part of a [[sequence]] which includes four Fermat primes (except for [[3]]) — is the fifth and largest known Fermat prime: [[65,537]].<ref>{{Cite OEIS |A014551 |Jacobsthal-Lucas numbers. |access-date=2023-06-29 }}</ref> It is one more than the smallest number with exactly seventeen [[divisor]]s, [[65,536 (number)|65,536]] = 2<sup>16</sup>.<ref>{{Cite OEIS |A005179 |Smallest number with exactly n divisors. |access-date=2023-06-28 }}</ref> Since seventeen 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]] and ultimately led him to choose mathematics over philology for his studies.<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><ref>[[Theoni Pappas|Pappas, Theoni]], ''Mathematical Snippets'', 2008, p. 42.</ref>' ]
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'1691048450'