17 ( seventeen ) is the natural number following 16 and preceding 18. It is prime.
In speech, the numbers 17 and 70 are often confused as they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 /sɛvɨnˈtiːn/ vs 70 /ˈsɛvɨnti/ . 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 /ˈsɛvɨntiːn/ .
The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena.
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, 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; in fact, it is the smallest prime not to be a Higgs prime for squares, and the smallest not to be a Higgs prime for 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.
Seventeen is the aliquot sum of two numbers, the odd discrete semiprimes 39 and 55 is the base of the 17-aliquot tree.
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 n 2 + n + p , for all positive n < p − 1.
In the Irregularity of distributions problem, 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).
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".
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."
Similar to Feller, Prof. Vadim Khayms of Stanford University is also known to use 17 as an arbitrary value during lectures. His Computational Mathematics for Engineers course includes 17 lectures.
17 is the least random number , according to the Hackers' Jargon File. There is a proven theorem 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.
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 x 3 + y 2 = 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 Kingdom, the minimum driving age for a car or van.
- In the United States, the age at which one may purchase M-rated video games according to ESRB ratings.
- Also in some of the states in the United States, seventeen is the age of consent.
- In most states of the United States and the United Kingdom, the age at which you may donate blood.
- In many countries and regions, the age at which one may obtain a driver's license.
- In the United States, the age at which one may rent or purchase R rated movies by himself/herself according to the MPAA film rating system.
- In the United States, the age at which one can enlist in the armed forces with Parental Permission.
In culture
Music
- 17 is a number of obsession used by horrorcore rappers, Insane Clown Posse. The song "17 Dead" off their first EP Beverly Kills 50187 uses the number frequently. Many of their songs reference the number 17 and most of their LP's contain 17 tracks. 17 is also used for the 17th Dimension in ICP's board game, the Quest for Shangri-La, as an infinite dimension of evil.
- "(She's) Sexy + 17" was a 1983 Top 10 hit for Stray Cats from the album Rant N' Rave with the Stray Cats .
- "At Seventeen" was a 1975 hit by Janis Ian.
- "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.
- "Seventeen" was the original name of The Beatles song "I Saw Her Standing There" which begins with the lyric "Well, she was just seventeen if you know what I mean."
- "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'.
- "17", a song recorded by Winger.
- "17", a song by yourcodenameis:milo.
- "Seventeen", a song by Ladytron.
- "Seventeen" by Jimmy Eat World.
- "Seventeen Ain't So Sweet" a song by The Red Jumpsuit Apparatus.
- "17" a song by Kings of Leon.
- "Edge of Seventeen", a song from the 1981 album Bella Donna by Stevie Nicks.
- "17" by Milburn.
- 17 Hippies, German band.
- "Seventeen Forever" a song by Metro Station (band).
- Seventeen Days , 3rd studio album from American rock band 3 Doors Down.
- "Dancing Queen" by Abba features the line 'You are the Dancing Queen, young and sweet, only 17'.
- "All Summer Long" by Kid Rock features the line 'She was 17 but she was far from in between'.
- "Strawberry Wine" by Deana Carter features the line 'Strawberry Wine, 17, the hot July moon saw everything'.
- "God Love Her" by Toby Keith features the line 'The way a girl gets when she turns 17, kinda crazy'.
- "Sheer Heart Attack" by Queen features the line 'Well you're just 17 and all you want to do is disappear'.
- "Seventeen" is the sixth song on the album Give Me a Wall by ¡Forward, Russia!.
- "Hello, Seventeen" by 12012.
- "17 Again" is a song by Eurythmics as featured on their 1999 album Peace .
- Seventeen Seconds is the second studio album by The Cure, released in April 1980 by Fiction Records.
- "17 Days" was a song recorded by Prince.
- "Seventeen" is the fifth song on the album Shaka Rock by the Australian rock band Jet.
- "Seventeen" is the 22nd musical number on the Repo! soundtrack.
Film
- Number Seventeen (1932), directed by Alfred Hitchcock
- Stalag 17 (1953), directed by Billy Wilder
- Try Seventeen (2002), directed by Jeffrey Porter
- 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 1
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