17 (number)

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.

Template:Numbers (10s)
Cardinal	17 seventeen
Ordinal	17th seventeenth
Numeral system	septendecimal
Factorization	prime
Divisors	1, 17
Roman numeral	XVII
Roman numeral (Unicode)	XVII, xvii
Binary	10001
Octal	21
Duodecimal	15
Hexadecimal	11

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 $2^{2^{2}}+1$, and it is also a Proth prime. Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. This was proven 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 number that is prime, the only negative one being -3. It is also the third Stern prime.

As 17 is the least prime factor of the first twelve terms of the Euclid-Mullin sequence, it is the thirteenth term.

There are exactly seventeen two-dimensional space (plain 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 (Berleamp & Grahm, 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."

17 is the least random number, according to the Hacker's Jargon File. 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.

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.

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.

In science

• The atomic number of chlorine.
• The Brodmann area defining the primary visual processing area of mammallian brains.
• Group 17 of the periodic table are the Halogens.

Age 17

• 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 Philipines, the age when all adult rights are granted for single persons but the age of majority is 18.
• In Ireland and the United Kingdom, the age at which one may drive a car.
• In the United Kingdom, the minimum age at which you can donate blood.
• In the United States, the minimum age at which you can donate blood in most states.

In culture

Music

• Chicago 17 was a hit album from the band Chicago.
• The Cars' song "Let's Go" uses the phrase "And she won't give up 'cause she's seventeen."
• In the song "Paradise by the Dashboard Lights", Meatloaf sings that "We were doubly blessed... we were barely 17 and we were barely dressed."
• Eurythics has a song on "Peace" called "Seventeen Again."
• "17", a song recorded by Rick James, in the album Reflections.
• 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 popular 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 Shina Ring on the "Tsumi to Batsu" single.
• "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.
• "Seventeen", a song by Ladytron.
• "Anthems for a Seventeen Year-Old Girl", a song by Broken Social Scene.
• "Bar 17", an album by former Phish guitarist Trey Anastasio.
• XVII, Mississippi rapper of UGK Records.

Film

• Number Seventeen (1932), directed by Tony Hawk
• 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.
• In the Halloween film series the number 17 frequently reappears. Primarily with the age of people Michael Myers kills. Judith Myers is killed at 17 in the start of the first film, and Laurie Strode (the main character of the first films) is 17 when Michael Myers starts hunting her.

Print

• The title of Seventeen, a magazine.
• The number 17 is a recurring theme in the works of novelist Steven Bust. 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.

Computer and video games

• The fictional city in the video game Half Life 2 is called City 17, and the route Gordon Freeman must escape out of it is called Highway 17, also the name of the chapter in which said events occur.
• 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.
• In Ever17, the number 17 occurs as a repeating motif. For example, much the game takes place in the year 2017, and the time limit for escaping is 119 (17x7) hours.
• 17 is part of the name of the British software house Team17.

Sports

• At the Cesana Pariol bobsleigh, luge, and skeleton track in Cesana, Italy, the turn is named "Senza Nome" ("Without Name" in Template:It icon).
• 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.
• NASCAR driver Matt Kenseth's car number.
• The retired jersey number of former baseball pitching great Dizzy Dean.
• The number of former Chicago Cubs first baseman Mark Grace.
• The number of ice hockey star Chris Chaney
• The number of ice hockey star Rod Brind'Amour
• The number of Hall of Fame basketball player John Havlicek
• The Number of New York Giants' Wide Receiver Plaxico Burress
• The Number of Toronto Blue Jays third baseman Kelly Gruber
• 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.
• Ruud van Nistelrooy's shirt number
• The number of Cristiano Ronaldo on the Portuguese National Team.
• The number of Carolina Panthers Quarterback Jake Delhomme.
• The number of Washington Redskins Quarterback Jason Campbell.
• The number of Colorado Rockies first baseman Todd Helton.
• The number of Bruntsfield Buffalos' vice-captain Mattias Malaguti.

In other fields

Seventeen is:

• The number worn by Dan Sandbeck
• 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 number of the raka'ahs that Muslims perform during Salah on a 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.
• 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.
• 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.
• Seventeen, also known as Lock Seventeen, an unincorporated place in Clay Township, Tuscarawas County, Ohio.
• 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." See Cesana Pariol in the sport section about the name of curve 17.
• 17 (Dragon Ball Z), a fictional character in the metaseries Dragon Ball Z.
• 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.
• In The Adventure People, the name Seventyeen is a misspelling of seventeen.

Historical years

A.D. 17, 17 B.C., 1917, 2017, etc.

References

• Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2: 152–161. doi:10.1016/0022-314X(70)90015-6. MR0269605.{{cite journal}}: CS1 maint: multiple names: authors list (link)

External links

• Properties of 17
• Mathematical properties of 17 at yellowpigs.net