17th century in Africa

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17 (seventeen) is the
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathematical terminology, w ...
following and preceding 18. It is a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. Seventeen is the sum of the first four prime numbers.

# In mathematics

Seventeen is the seventh
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. The next prime is nineteen, with which it forms a
twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pri ...
. Seventeen is a
permutable prime A permutable prime, also known as anagrammatic prime, is a prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater tha ...
and a supersingular prime. Seventeen is the third
Fermat prime In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gen ...
, as it is of the form 2 + 1, specifically with ''n'' = 2. Since 17 is a Fermat prime, regular
heptadecagon In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of ...

s can be 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. There are exactly 17 two-dimensional space (plane symmetry) group (mathematics), groups. These are sometimes called wallpaper groups, 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 + ''n'' + ''p'', for all positive ''n'' < ''p'' − 1. Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathematical terminology, w ...
s with this property. The Platonists 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". 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. 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 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.

# 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, and some jurisdictions around the world, 17 is the age of consent, age of sexual consent * 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

### 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

## 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 Leon Kass, 17 has some significant meaning (as yet not known exactly) in the book of Genesis. * 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. * In the Yasna of Zoroastrianism, seventeen chapters were written by Zoroaster himself. These are the Gathas. * The number of the raka'ahs that Muslims perform during Salat on a daily basis. * The number of surat 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.

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