17 (number)

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Cardinal	seventeen
Ordinal	17th (seventeenth)
Numeral system	septendecimal
Factorization	prime
Divisors	1, 17
Greek numeral	ΙΖ´
Roman numeral	XVII
Binary	100012
Ternary	1223
Quaternary	1014
Quinary	325
Senary	256
Octal	218
Duodecimal	1512
Hexadecimal	1116
Vigesimal	H20
Base 36	H36

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

In English speech, the numbers 17 and 70 are sometimes confused, as they sound very similar.

The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. Seventeen is the sum of the first four prime numbers.

In mathematics[edit]

Seventeen is the seventh prime number. The next prime is nineteen, with which it forms a twin prime.

Seventeen is the third Fermat prime, as it is of the form 2²ⁿ + 1, specifically with n = 2.^[1] Since 17 is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss.^[2]

There are exactly 17 two-dimensional space (plane symmetry) groups. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.

Like 41, the number 17 is a prime that yields primes in the polynomial n² + 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 numbers 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".^[3]

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.^{[4][unreliable source?]}

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 x³ + y² = n has two different solutions for x and y positive integers. The next such number is 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.)

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.

In science[edit]

• The atomic number of chlorine
• The Brodmann area defining the primary visual processing area of mammalian brains
• Group 17 of the periodic table is called the halogens
• The number of elementary particles in the Standard Model of physics^[5]

In languages[edit]

Grammar[edit]

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[edit]

• In the UK, the minimum age for taking 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 M-rated video games without parental consent
• In some US states,^[6] and some jurisdictions around the world, 17 is the age of sexual consent^[7]
• 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 R-rated movies without parental consent
• 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, the voting age
• In Chile, the minimum driving age.

In culture[edit]

Music[edit]

Bands[edit]

• 17 Hippies, a German band
• Sytten (17 in Norwegian), a Norwegian-American rapper
• Seventeen (세븐틴), a South Korean boy band
• Heaven 17, an English new wave band
• East 17, an English boy band

Albums[edit]

• 17 (XXXTentacion album), an album by XXXTentacion
• 17 (Motel 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

Songs[edit]

• "17" (Sky Ferreira song)
• "17" (Yourcodenameis:Milo song)
• "17 Again", a song by Eurythmics
• "17 år", a song by Veronica Maggio
• "17 Crimes", a song by AFI
• "17 Days", a song by Prince
• "17", a song by Dan Bălan
• "17", a song by Jethro Tull
• "17", a song by Kings of Leon
• "17", a song by Milburn
• "17", a song by Rick James from 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
• "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" (Ladytron 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
• "Seventeen", a song by Mat Kearney from the iTunes edition of Young Love
• "Seventeen", a song from the 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

Other[edit]

• Seventeen (musical), a 1951 American musical
• The ratio 18:17 was a popular approximation for the equal tempered semitone during the Renaissance

Film[edit]

• Seventeen (1916), an adaptation of the novel of the same name by Booth Tarkington
• Number 17 (1928), a British-German film
• Number Seventeen (1932), directed by Alfred Hitchcock
• Seventeen (1940), a second adaptation of the Tarkington novel
• Number 17 (1949), a Swedish film
• Stalag 17 (1953), directed by Billy Wilder
• 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 (2009), directed by Burr Steers

Anime and manga[edit]

• Android 17, a character from the Dragon Ball series
• Detective Konawaka from the Paprika anime has a strong dislike for the number 17

Games[edit]

• The computer game Half-Life 2 takes place in and around City 17
• The visual novel Ever17 strongly revolves around the number 17

Print[edit]

• The title of 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 "23/17 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 British wizards' currency

Religion[edit]

• According to Leon Kass, 17 has some significant meaning (as yet not known exactly) in the book of Genesis.^[8]
• 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.^[9]
• 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[edit]

• 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 achieved.

In other fields[edit]

Seventeen is:

• Described at MIT as 'the least random number', according to the Jargon File.^[10] 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.^[11]
• 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 the Second World War, 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 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)

• 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 implying "My life is over." (c.f. "Vixerunt", Cicero's famous announcement of an execution.) Renault sold its "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 cicadas 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,^[12][13]

References[edit]

• Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. Bibcode:1970JNT.....2..152B. doi:10.1016/0022-314X(70)90015-6. MR 0269605. 

External links[edit]

Wikimedia Commons has media related to 17 (number).

Look up seventeen in Wiktionary, the free dictionary.

• Properties of 17
• Mathematical properties of 17 at yellowpigs.net
• 17
• is 17 the most random number at the wayback machine.