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17 (number)

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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
Factorization prime
Divisors 1, 17
Roman numeral XVII
Binary 10001
Octal 21
Hexadecimal 11

In mathematics

Seventeen is the 7th prime number. The next prime is nineteen, with which it comprises 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  .

17 is the third Fermat prime. Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. This was proved by Karl Friedrich Gauss. 17 is the second and last Genocchi prime. 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.

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! = 355687428096000

It is a repunit in hexadecimal.

In science

Astronomy

In human affairs: 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 Kingdom, the age at which one may drive a car.

In other fields

Seventeen is:

  • 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.
  • 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 guns in a 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.
  • 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 title of At Seventeen, a famous song by Janis Ian.
  • 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 of trees Dostoevsky could see out of the window of his cell while he was in prison.
  • The number of special significance to the Yellow Pig Day.
  • NASCAR driver Matt Kenseth's car number.
  • The number which held the key to the control of natural forces in Godley & Creme's Consequences.
  • Historical years: A.D. 17, 17 B.C., or 1917
  • A number of great significance to horror-core band Insane Clown Posse
  • 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)
  • The retired jersey number of former baseball pitching great Dizzy Dean
  • 17 plays a role in most of the works of novelist Steven Brust. All his novels have 17 or 34 (17×2) chapters, except for one that was not divided into chapters, and 17 is holy in his Drageara setting.
  • 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.) In Italy, it is not uncommon to notice that buildings do not have 17th floor, hotels do not have a room 17. The Italian airline carrier, Alitalia, does not have a seat 17. Renault sold its "R17" model in Italy as "R177."
  • 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 film Three Days of the Condor, the title character played by Robert Redford works in section 17 of the CIA.
  • The title of the song "17" by the Smashing Pumpkins. It is 17 seconds long, with no vocals, but comes with a poem in which read at a standard speed will finish at the end of the song.
  • Part of a song title by Harry Chapin, "She is always seventeen".
  • The age of the "Dancing Queen" in the hit ABBA song of the same name.
  • The age of the girl in The Beatles' "I Saw Her Standing There."
  • The number of the hen house that is transformed into an airplane at "Chicken Run".
  • The number of pins in an iPod connecting cable.
  • A song recorded by Winger.
  • In Half-Life and Half-Life 2, City 17 is the name of the Combine city.
    • Also, the highway is called Highway 17
  • In 2004 Volatile films released a feature length film titled The Significance of Seventeen starring Cindy Taylor; the film does address the high incidence of the number 17 and its function as 'the most random number' as described by MIT.

References

Berlekamp, E. R. and Graham, R. L., Irregularities in the distributions of finite sequences, J. Number Theory 2 (1970), 152–161.

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