17 (number)

← 16 18 → 17
← 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	seventeen
Ordinal	17th (seventeenth)
Numeral system	septendecimal
Factorization	prime
Divisors	1, 17
Roman numeral	XVII
Binary	100012
Octal	218
Duodecimal	1512
Hexadecimal	1116

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

In spoken English, the numbers 17 and 70 are sometimes confused because 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 3n − 1.

17 is the third Fermat prime, as it is of the form 2⁴ + 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 n² + 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.

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 mammalian brains.
• Group 17 of the periodic table is called the halogens.

Age 17

• In the United Kingdom, the minimum driving age for a car or van.
• In the United States, it is the age at which one may purchase, rent, or reserve M-rated video games without parental consent.
• Also in some of the states in the United States and many jurisdictions around the world, seventeen is the age of consent.
• In most states of the United States, Canada and in the United Kingdom, the age at which you may donate blood (without parental consent).
• 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 watch, rent, or purchase R-rated movies without parental consent.
• In the United States, the age at which one can enlist in the armed forces with parental permission.
• At this age one can apply for a Private Pilot Licence (however the applicant can start training at 16).

In culture

Music

• "Only 17" By Rucka Rucka Ali
• "(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 by Jethro Tull.
• "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'.
• "Seventeen", 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.
• "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.
• "17" is a song by Moldovan singer Dan Bălan
• "17 år" (17 years) is a song by Swedish singer Veronica Maggio on her 2008 sohopmore album "Och vinnaren är..." (And the winner is...).
• A song by American singer Sky Ferreira.
• "Only Seventeen", a song by Skid Row.
• "When I Was Seventeen", a song by Frank Sinatra
• "Seventeen", the twelfth track on the US edition of the album "The Family Jewels" by Marina & the Diamonds.

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 Halloween H20, Laurie Strode also known as Keri Tate, reveals her true identity to her boyfriend, Will. She tells him that she is related to Michael Myers and mistakenly says that her older sister, Judith Myers, died at the age of 17 years. However, in Halloween (1978), the dates on Judith's tombstone read November 10, 1947 - October 31, 1963. That would have meant that Judith was 15 years old at the time of her death. However, it is probable that the script writers wrote Judith's age as 17 so that it would correspond with Laurie Strodes age from the original film.
• 17 Again (2009), directed by Burr Steers

Anime and manga

• Android 17, a character from the Dragon Ball series.
• Detective Konawaka from the Paprika anime has a strong dislike for the number 17.

Games

• The computer game Half-Life 2 takes place in and around City 17.

Print

• The title of Seventeen, a magazine.
• The title of Just Seventeen, a former magazine.
• The number 17 is a recurring theme in 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 Harry Potter universe
  • 17 is the coming of age for wizards. It is equivalent to the usual coming of age at 18.
  • 17 is the number of Sickles in one Galleon in the British wizards' currency

Religion

• According to Leon Kass, 17 has some significant meaning (as yet not known exactly) in the book of Genesis.
• In the Yasna of Zoroastrianism seventeen chapters were written by Zoroaster himself, these are the Gathas.
• The number of the raka'ahs that Muslims perform during Salah on a daily basis.
• The number of surat al-Isra in the Qur'an.

In sports

• 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 pitcher Dizzy Dean.
• 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.

In other fields

Seventeen is:

• Described at MIT as 'the least 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.
  • This study has been repeated a number of times.
• 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.
• The number of flames emanating from the grenade cap-badge of the Grenadier Guards.
• 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.
• 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.
• "Highway 17" or "Route 17": See List of highways numbered 17 and List of public transport routes numbered 17.
• Seventeen, also known as Lock Seventeen, an unincorporated place in Clay Township, Tuscarawas County, Ohio.
• 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 anagrammatically to VIXI, which in the Latin language it translates to "I have lived", the perfect implying "My life is over." (c.f. "Vixerunt", Cicero's famous announcement of an execution.) Renault sold its "R17" model in Italy as "R177." See Cesana Pariol in the sport section about the name of curve 17.
• The fear of the number 17 is called 'heptadecaphobia' or 'heptakaidekaphobia'.
• 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 of special significance to Yellow Pig's Day and Hampshire College Summer Studies in Mathematics.
• The number to call Police in France.
• Force 17, a special operations unit of the Palestinian Fatah movement.
• The number of the French department Charente-Maritime
• A slang term in the medical field for a psychiatric patient

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 (2): 152–161. doi:10.1016/0022-314X(70)90015-6. MR0269605. 

External links

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