# 17 (number)

17 (seventeen) is the natural number following 16 and preceding 18.

 Template:Numbers 10s Cardinal 17seventeen Ordinal 17thseventeenth Factorization prime Divisors 1, 17 Roman numeral XVII Binary 10001 Octal 21 Hexadecimal 11
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## In mathematics

Seventeen is the 7th smallest 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 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.

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).

## In science

In 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 (http://www.ngcic.org/) NGC 17, a peculiar galaxy in the constellation Cetus
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) 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 (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) 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.

## 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:

• Described at MIT as 'the least random number', according to hacker's lore.
• 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 swear word in Swedish. The origin is debated, and is commonly used as "sjutton också!" ("seventeen, too!"). 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 title of At Seventeen, a famous song by Janis Ian.
• The title of Seventeen, a magazine.
• A name of a proliferic pornographic film company, which specialises in young (but above the age of consent) natural looking teens. They make magazines too, which shouldn't be confused with the above magazine.
• 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.
• 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)

## 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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