17 (number)

17 (seventeen) is the natural number following 16 and preceding 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,^[1] as seven is itself prime. It forms a twin prime with 19,^[2] a cousin prime with 13,^[3] and a sexy prime with both 11 and 23.^[4] 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 ${\displaystyle k^{2}-k+41}$,^[5] and the sixth Mersenne prime exponent, which yields 131,071.^[6] It is also the minimum possible number of givens for a sudoku puzzle with a unique solution.^[7][8] 17 can be written in the form ${\displaystyle x^{y}+y^{x}}$ and ${\displaystyle x^{y}-y^{x}}$; and as such, it is a Leyland prime and Leyland prime of the second kind:^[9][10]

${\displaystyle 2^{3}+3^{2}=17=3^{4}-4^{3}}$

The number of integer partitions of 17 into prime parts is 17 (the only number ${\displaystyle n}$ such that its number of such partitions is ${\displaystyle n}$).^[11]

Seventeen is the third

${\displaystyle 2^{2^{n}}+1}$

${\displaystyle n=2}$

Seventeen is the minimum number of vertices on a graph such that, if the edges are colored with three different colors, there is bound to be a monochromatic triangle; see Ramsey's theorem.^[18]

There are also:

• Seventeen crystallographic space groups in two dimensions.^[19] These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.

• Seventeen combinations of regular polygons that completely
  regular and semiregular tilings, while 6 of these (3.7.42,^[21] 3.8.24,^[22] 3.9.18,^[23] 3.10.15,^[24] 4.5.20,^[25] and 5.5.10)^[26] exclusively surround a point in the plane and fill it only when irregular polygons are included.^[27]

• Seventeen orthogonal curvilinear
  Laplace equation can be solved using the separation of variables
  technique.

• Seventeen distinct fully supported stellations generated by an icosahedron.^[28] The seventeenth prime number is 59, which is equal to the total number of stellations of the icosahedron by Miller's rules.^[29][30] Without counting the icosahedron as a zeroth stellation, this total becomes 58, a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17).^[31]

Seventeen distinct fully supported stellations are also produced by truncated cube and truncated octahedron.^[28]

• Seventeen four-dimensional
  Minkowski sums of zonotopes with the 24-cell, itself the simplest parallelotope that is not a zonotope.^[32]

Seventeen is the highest dimension for

paracompact Vineberg polytopes

with rank ${\displaystyle n+2}$ mirror

Seventeen is the longest sequence for which a solution exists in the irregularity of distributions problem,^[34] while the sequence of residues (mod n) of a googol and googolplex, for ${\displaystyle n=1,2,3,...}$, agree up until ${\displaystyle n=17}$.

In

A positive definite quadratic integer matrix represents all 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, 61, and 71).^[37]

In science

• The atomic number of chlorine.
• The Brodmann area defining the primary visual processing area of mammalian brains.
• halogens
  .
• The number of elementary particles with unique names in the Standard Model of physics.^[38]

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.

Age 17

• In most countries across the world, it is the last age at which one is considered a minor under law.
• 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,^[39] and some jurisdictions around the world, 17 is the age of sexual consent^[40]
• 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
• 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
  Timor-Leste, the age of majority

Bands

• 17 Hippies, a German 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 (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
• Sector 17, a 2022 repackaged album by Seventeen

Songs

• "17 Again", a song by Tide Lines
• "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
  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
• "Seventeen", a song performed by
  Marina and the Diamonds
• "Seventeen" and "Seventeen (Reprise)", songs in the musical Heathers
• "Seventeen" and "Seventeen (Reprise)", songs in the musical Tuck Everlasting

Other

• Seventeen, 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
• 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

• The computer game
  City 17
• The visual novel Ever 17: The Out of Infinity 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
  Dragaera
  , where the number is considered holy.
• In
  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
  epogdoon by its division into unequal intervals.^[41]
• In the
  Gathas
  .
• The number of the
  Salat
  on a daily basis.
• The number of
  Qur'an
  .

In sports

• 17 is the number of the longest winning streak in NHL history, which the Pittsburgh Penguins achieved in 1993.
• 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 season, Formula One drivers have been able to choose 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.^[42]
  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.[43]
• 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
  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)
  .

• In
  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 to call police in France.
• Force 17, a special operations unit of the Palestinian Fatah movement.
• The number of the French department Charente-Maritime.
• Boeing 777-200ER
  , was on 17 July 1997, exactly 17 years prior to the doomed flight.

References

1. ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-29.
2. ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
3. ^ Sloane, N. J. A. (ed.). "Sequence A046132 (Larger member p+4 of cousin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
4. ^ Sloane, N. J. A. (ed.). "Sequence A023201 (Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
5. ^ Sloane, N. J. A. (ed.). "Sequence A014556 (Euler's "Lucky" numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
6. ^ Sloane, N. J. A. (ed.). "Sequence A000043 (Mersenne exponents)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
7. arXiv:1201.0749 [cs.DS
   ].
8. S2CID 8973439
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9. ^ Sloane, N. J. A. (ed.). "Sequence A094133 (Leyland primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
10. ^ Sloane, N. J. A. (ed.). "Sequence A045575 (Leyland primes of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
11. ^ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-12.
12. ^ "Sloane's A019434 : Fermat primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
13. ^ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-29.
14. ^ Sloane, N. J. A. (ed.). "Sequence A005179 (Smallest number with exactly n divisors.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-28.
15. ^ 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."
16. ^ Pappas, Theoni, Mathematical Snippets, 2008, p. 42.
17. ^ Babbitt, Frank Cole (1936). Plutarch's Moralia. Vol. V. Loeb.
18. ^ Sloane, N. J. A. (ed.). "Sequence A003323 (Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
19. ^ Sloane, N. J. A. (ed.). "Sequence A006227 (Number of n-dimensional space groups (including enantiomorphs))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-25.
20. ^ Dallas, Elmslie William (1855), The Elements of Plane Practical Geometry, Etc, John W. Parker & Son, p. 134.
21. ^ "Shield - a 3.7.42 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
22. ^ "Dancer - a 3.8.24 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
23. ^ "Art - a 3.9.18 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
24. ^ "Fighters - a 3.10.15 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
25. ^ "Compass - a 4.5.20 tiling". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
26. ^ "Broken roses - three 5.5.10 tilings". Kevin Jardine's projects. Kevin Jardine. Retrieved 2022-03-07.
27. ^ "Pentagon-Decagon Packing". American Mathematical Society. AMS. Retrieved 2022-03-07.
28. ^ ^{a b} Webb, Robert. "Enumeration of Stellations". www.software3d.com. Archived from the original on 2022-11-26. Retrieved 2022-11-25.
29. ISBN 978-1-4613-8216-4
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30. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-17.
31. ^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-02-17.
32. MR 0768703
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33. doi:10.1023/B:MATN.0000030993.74338.dd
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34. MR 0269605
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36. ^ Sloane, N. J. A. (ed.). "Sequence A258706 (Absolute primes: every permutation of digits is a prime. Only the smallest representative of each permutation class is shown.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-29.
37. ^ Sloane, N. J. A. (ed.). "Sequence A154363 (Numbers from Bhargava's prime-universality criterion theorem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
38. ^ Glenn Elert (2021). "The Standard Model". The Physics Hypertextbook.
39. ^ "Age Of Consent By State". Archived from the original on 2011-04-17.
40. ^ "Age of consent for sexual intercourse". 2015-06-23.
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42. ^ "random numbers". catb.org/.
43. ^ "The Power of 17". Cosmic Variance. Archived from the original on 2008-12-04. Retrieved 2010-06-14.

• MR 0269605
  .

External links

Wikimedia Commons has media related to 17 (number).

Look up seventeen in Wiktionary, the free dictionary.

• Properties of 17
• Mathematical properties of 17 Archived 2019-07-29 at the Wayback Machine at yellowpigs.net
• 17
• is 17 the most random number at the wayback machine.
• Number 17 at the Database of Number Correlations
• Prime Curios for the number 17