17 (number)

← 16 17 18 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventeen
Ordinal	17th (seventeenth)
Numeral system	septendecimal
Factorization	prime
Divisors	1, 17
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 spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 /sɛvənˈtiːn/ vs 70 /ˈsɛvənti/. However, in dates such as 1789 or when contrasting numbers in the teens, such as 16, 17, 18, the stress shifts to the first syllable: 17 /ˈsɛvəntiːn/.

The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. In a 24-hour clock, the seventeenth hour is in conventional language called five or five o'clock.

In mathematics

Seventeen is the 7th prime number. The next prime is nineteen, with which it forms a twin prime. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071. 17 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.

17 is the third Fermat prime, as it is of the form 2²ⁿ + 1, specifically with n = 2,^[1] and it is also a Proth prime.^[2] Since 17 is a Fermat prime, regular heptadecagons can be constructed with compass and unmarked ruler. This was proven by Carl Friedrich Gauss.^[3] Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes; in fact, it is the smallest prime not to be a Higgs prime for squares, and the smallest not to be a Higgs prime for cubes.

17 is the only positive Genocchi number that is prime, the only negative one being −3. It is also the third Stern prime.^[4]

17 is the average of the first two Perfect numbers.

17 is the thirteenth term of the Euclid–Mullin sequence.^[5]

Seventeen is the aliquot sum of the semiprime 39, and is the aliquot sum of the semiprime 55, and is the base of the 17-aliquot tree.

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.

In the Irregularity of distributions problem, consider a sequence of real numbers between 0 and 1 such that the first two lie in different halves of this interval, the first three in different thirds, and so forth. The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).

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".^[6]

17 is the tenth Perrin number, preceded in the sequence by 7, 10, 12.^[7]

In base 9, the smallest prime with a composite sum of digits is 17.

17 is the least random number,^[8] according to the Hackers' Jargon File.

It is a repunit prime in hexadecimal (11).

17 is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved in 2012.^[9]

There are 17 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the 3-variable Laplace equation can be solved using the separation of variables technique.

17 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.

17 is the minimum number of vertices on a graph such that, if the edges are coloured with 3 different colours, there is bound to be a monochromatic triangle. (See Ramsey's Theorem.)

17 is a full reptend prime in base 10, because its repeating decimal is 16 digits long.

In science

• 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.^[10]

In languages

Grammar

In French, 17 is the first compound number (dix-sept). The numbers 11 (onze) through 16 (seize) have their own names.

Age 17

• In the UK, the minimum driving age for a car or 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.
• Also, in some US states,^[11] and some jurisdictions around the world, 17 is the age of sexual consent.^[12]
• In most US states, Canada and in the UK, the age at which one may donate blood (without parental consent).
• In many countries and regions, 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.
• At this age one can apply for a Private Pilot Licence (however the applicant can start training under this age.)
• In Greece, the voting age.

In culture

Music

Bands

• 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

• 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

• "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
• "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
• "(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

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

Film

• 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.
• In Halloween H20, Laurie Strode also known as Keri Tate, reveals her true identity to her boyfriend, Will. She tells him that she is related to Michael Myers and mistakenly says that her older sister, Judith Myers, died at the age of 17 years. However, in Halloween (1978), the dates on Judith's tombstone read November 10, 1947 - October 31, 1963. That would have meant that Judith was 15 years old at the time of her death. However, it is probable that the script writers wrote Judith's age as 17 so that it would correspond with Laurie Strodes age from the original 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 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 Ever17 strongly revolves around the number 17.

Print

• 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

• According to Leon Kass, 17 has some significant meaning (as yet not known exactly) in the book of Genesis.^[13]
• 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.^[14]
• 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.
• The number of rays in the Vergina Sun, symbol by Philip's Argead dynasty, possible religious symbol representing the Olympian gods.

In sports

• The most famous Ford number in the V8 Supercar championship, Driven by Dick Johnson to bring 5 Australian Touring Car Championships to his name. Now driven by son Steven Johnson.
• The number of a car in the NASCAR Sprint Cup Series owned by Roush Fenway Racing since 1999, Matt Kenseth has driven the car since its debut in 1999 until 2012. Consideration of replacing the number with the traditional Roush #6 for the 2013 season with new driver Ricky Stenhouse, Jr. has been considered.
• From 1987 until 2001, Hendrick Motorsports has used #17 for various drivers in the NASCAR Hall of Fame from 1987–90, and for a satellite team from 1991-92. It was also used by the team owner's son, who died in 2004.
• The jersey number 17 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The St. Louis Cardinals, for Hall of Famer Dizzy Dean, who also had a notable career as a broadcaster for the team.
    • The Colorado Rockies, for Todd Helton (number retired on August 17, 2014).
  • In the NBA:
    • The Boston Celtics, for Hall of Famer John Havlicek.
    • The Golden State Warriors, for Hall of Famer Chris Mullin.
    • The Los Angeles Lakers have not retired #17. However, the team has honored the number for Hall of Famer Jim Pollard, who wore it when the franchise was the Minneapolis Lakers.
  • In the NHL:
    • The Carolina Hurricanes, for Rod Brind'Amour.
    • The Edmonton Oilers, for Hall of Famer Jari Kurri.
  • No NFL team has retired the number.
• The number that footballer Marc-Vivien Foé wore for the French clubs Lens and Lyon, retired by both clubs after his death from heart failure during a semifinal match in the 2003 FIFA Confederations Cup. Foé also wore the 17 shirt for the Cameroon national team at the time of his death.
• Larry Ellison's victorious 2013 Americas Cup Oracle racing yacht bears the name "17".
• Jules Bianchi ran the number 17 in the 2014 Formula One season, driving for Marussia. After his death in July 2015 from injuries sustained in the 2014 Japanese Grand Prix, the number was retired by the FIA

In other fields

Seventeen is:

• Described at MIT as 'the least random number', according to hackers' lore. 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.^[15]
• 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).

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 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.

References

1. "Sloane's A019434 : Fermat primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
2. "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
3. 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 polygon) could be constructed with ruler and compasses."
4. "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. "Sloane's A000945 : Euclid-Mullin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
6. Babbitt, Frank Cole (1936). "Plutarch's Moralia". V. Loeb.
7. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
8. "random numbers". catb.org/.
9. McGuire, Gary. "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem" (PDF). arXiv:1201.0749. Retrieved 26 March 2012.
10. Glenn Elert. "The Standard Model".
11. "Age Of Consent By State".
12. "Age of consent for sexual intercourse".
13. For example, the patriarch Jacob lived 17 years after his son Joseph went missing and presumed dead, and lived 17 years after their reunion in Egypt, and the lifespans of Abraham aged 175, Isaac aged 180, and Jacob aged 147 are not a coincidence. "(The sum of the factors in all three cases is 17; of what possible significance this is, I have no idea.)" Leon Kass, The beginning of wisdom: reading Genesis,(Simon and Schuster, 2003), ISBN 978-0-7432-4299-8, p. 413 n. 10 (citing Genesis 47:28), quote from p. 629 n. 18, found at Google Books. Retrieved June 17, 2009.
14. Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
15. "The Power of 17". Cosmic Variance.

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

External links

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