17 (number)

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17	10	7

17 (seventeen) is the natural number following 16 and preceding 18. In English, it is the smallest number with nine letters when spelled out.

← 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	17 seventeen
Ordinal	17th seventeenth
Factorization	prime
Divisors	1, 17
Roman numeral	XVII
Roman numeral (Unicode)	XVII, xvii
Binary	10001
Octal	21
Duodecimal	15
Hexadecimal	11

Look up seventeen in
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1 In mathematics
2 In science
- 2.1 Astronomy
3 Age 17
4 In culture
5 Historical years
6 References
7 External links

[edit] 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 $3 n - 1$ .

17 is the third Fermat prime. Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. This was proved by Carl Friedrich Gauss. Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes.

17 is the only positive Genocchi prime, the only negative one being -3. It is also the third Stern prime.

There are exactly seventeen 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.

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).

16 and 18 unit squares can each be formed into rectangles with perimeter equal to the area; and they are the only solutions. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch explains that 17 is therefore an unlucky number.

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

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

17 is known as the Feller number, after the famous mathematician William Feller who taught at Princeton University for many years. Feller would say, when discussing an unsolved mathematical problem, that if it could be proved for the case n = 17 then it could be proved for all positive integers n. He would also say in lectures, "Let's try this for an arbitrary value of n, say n=17." There is an unproved conjecture that 17 is the value most likely to be picked as a "random" number when such is needed in journalism which is derived from the Feller number.^[1]

17! = 355687428096000

It is a repunit prime in hexadecimal (11).

It is believed that the minimum possible number of givens for a sudoku puzzle with a unique solution is 17, but this has yet to be proven.

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.

[edit] In science

The atomic number of chlorine.
Group 17 represents the halogens in the periodic table.
The Brodmann area defining the primary visual processing area of mammallian brains.

[edit] Astronomy

Messier object M17, a magnitude 7.0 nebula/cluster in the constellation Sagittarius, also known as the Omega Nebula.

The New General Catalogue object NGC 17, a peculiar galaxy in the constellation Cetus

The Saros number of the solar eclipse series which began on -2427 July 3 and ended on -1111 September 1. The duration of Saros series 17 was 1316.2 years, and it contained 74 solar eclipses.

The Saros number of the lunar eclipse series which began on -2089 May 4 and ended on -809 June 10. The duration of Saros series 17 was 1280.1 years, and it contained 72 lunar eclipses.

[edit] Age 17

In the United States, the age at which one may donate blood and join the military voluntarily.
In the United States, the age at which one may view R-rated movies without a parent's accompaniment according to MPAA standards.
In the United States, the age at which one may purchase M-rated video games according to ESRB ratings.
In the United Kingdom, the age at which one may drive a car.

[edit] In culture

[edit] Music

The ratio 18/17 was a popular approximation for the equal tempered semitone during the Renaissance.
The age of the "Dancing Queen" in the hit ABBA song of the same name.
"Seventeen" was the original name of The Beatles song "I Saw Her Standing There".
Part of a song title by Harry Chapin, "She is Always Seventeen".
Seventeen Seconds, an album by The Cure.
The number which held the key to the control of natural forces in Godley & Creme's Consequences.
The band Heaven 17 derived their name from a fictional band mentioned in the novel and movie A Clockwork Orange.
"At Seventeen", a popular song by Janis Ian.
"Edge of Seventeen", a song by Stevie Nicks.
"Dreamy 17", a song by River City Rebels.
"It Was a Very Good Year", a song by Ervin Drake and made famous by Frank Sinatra who wistfully recalls "when I was seventeen...".
"17", a B-Side by Shiina Ringo on the "Tsumi to Batsu" single.
The title of the song "17" by the Smashing Pumpkins. It is 17 seconds long, with no vocals, but comes with a poem which read at a standard speed will finish at the end of the song. This song is also a musical allusion to another Smashing Pumpkins work called "Blissed and Gone" which references 17 in the lines "Sweet 17, sour 29" and "I had no cause, just 17 days of rain".
"Sexy & 17", a song by The Stray Cats.
In the song "Why Does It Always Rain On Me?" by Scottish band Travis, the answer to the song's title question is answered by,"Is it because I lied when I was seventeen?".
"17", a song recorded by Winger.
"17", a song by yourcodenameis:milo.
17, a song by The Regents

[edit] Film

Number Seventeen (1932), directed by Alfred Hitchcock
Stalag 17 (1953), directed by Billy Wilder
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.
The number of the hen house that is transformed into an airplane at "Chicken Run".

[edit] Print

The title of Seventeen, a magazine.
A name of a prolific pornographic film company, which specialises in young (but above the age of consent), natural looking teens. They also make magazines, which shouldn't be confused with the above subscription.
The number 17 is a recurring theme 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 novel So Long, and Thanks for All the Fish by Douglas Adams, a character who is, unknowingly, a rain god, has a numerical scheme to categorize all the different types of rain which continuously bombard him; the worst, the heaviest, the least pleasant, is Rain Type 17, "a dirty blatter blattering against the windows so hard, it was impossible to tell whether he had the wipers on or off."
In the Harry Potter universe, 17 is the coming of age for wizards. It is equivalent to the usual coming of age at 18.

[edit] Computer and Video Games

The fictional city in the video game Half Life 2 is called City 17.
In the Dreamcast and GameCube RPG Skies of Arcadia/Skies of Arcadia Legends, the three main characters, Vyse, Aika, and Fina, are all 17 years old.

[edit] Sports

The most famous Ford number in the V8 Supercar championship, Driven by Dick Johnson to bring 7 Australian Touring Car Championships to his name. Now driven by son Steven Johnson.
NASCAR driver Matt Kenseth's car number.
The retired jersey number of former baseball pitching great Dizzy Dean.
The number of ice hockey star Chris Chaney
The number of ice hockey star Rod Brind'Amour

[edit] In other fields

Seventeen is:

Described at MIT as 'the most 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.
The numbet of the raka'ahs that muslim perform in Salah on daily basis.
The number of laws of the game in Association Football
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.
A mild swear word in Swedish. The origin is debated, and is commonly used as "sjutton också!" ("seventeen, too!"). It can roughly be translated to "Darn!". It is of course also used for the number 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.
The designation of United States Interstate 17, a freeway in Arizona.
The designation of U.S. Route 17, a highway that runs from Virginia to Florida.
The number of trees Dostoevsky could see out of the window of his cell while he was in prison.
The number of special significance to Yellow Pig's Day and Hampshire College Summer Studies in Mathematics.
The number of surat al-Isra in the Qur'an.
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 anagramtically to VIXI, which in the Latin language it translates to "I have lived", the perfect tense implying "My life is over." (c.f. "Vixerunt", Cicero's famous announcement of an execution.) The Italian airline carrier, Alitalia, does not have a seat 17. Renault sold its "R17" model in Italy as "R177."
The number of pins in an iPod connecting cable.
The right age to start having sex according to Chef in the television series South Park
*Android 17 of the Dragonball Z television series.
Some species of cicadas have a life cycle of 17 years (ie they are buried in the ground for 17 years between every mating season).
The number to call Police in France