17 (number)

 ← 16 17 18 →
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
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 /sɛvənˈtn/ 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 /ˈsɛvəntn/.

The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. 17 is the sum of the first 4 prime numbers.

In mathematics

Seventeen is the 7th prime number, the next prime is nineteen, with which it forms a twin prime.

17 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 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]

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.[4]

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 sixth Mersenne prime exponent, yielding 131071.

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 the only prime number which is the sum of four consecutive primes (2,3,5,7). Any other 4 consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime.

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 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.
• Also, 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.
• At this age one can apply for a Private Pilot Licence (however the applicant can start training below this age.)
• In Greece, the voting age.
• In Chile, the minimum driving 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

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.[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

• 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".
• The number 17 has been retired in Formula 1 following Jules Bianchi's fatal accident in the 2014 Japanese Grand Prix who used number 17 in his F1 career since 2014.
• One of Cricket's best batsmen, AB de Villiers uses only 17 number jersey for any team he is playing for (Whether its for his national team South Africa or any franchise around the globe hiring him). AB17 is even famous as a nickname in the world of Cricket.

In other fields

Seventeen is:

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.
• Seventeen is Holland porn-video company.

References

1. ^ "Sloane's A019434 : Fermat primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
2. ^ 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."
3. ^ Babbitt, Frank Cole (1936). "Plutarch's Moralia". V. Loeb.
4. ^ McGuire, Gary. "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem" (PDF). arXiv:. Retrieved 26 March 2012.
5. ^ Glenn Elert. "The Standard Model".
6. ^
7. ^
8. ^ 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.
9. ^ Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
10. ^ "random numbers". catb.org/.
11. ^ "The Power of 17". Cosmic Variance.