Seventeen is: Described at MIT as 'the least random number', according to the Jargon File. 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.
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.
Seventeen is the sum of the first four prime numbers.
In mathematics [ edit ]
17 is the seventh prime number, which makes seventeen the fourth super-prime, as seven is itself prime. The next prime is 19, with which it forms a twin prime.[1] It is a cousin prime with 13 and a sexy prime with 11 and 23.[2][3] It is an emirp, and more specifically a permutable prime with 71, both of which are also supersingular primes.[4][5]
Seventeen is the only prime number which is the sum of four consecutive primes: 2,3,5,7. Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime.
Seventeen can be written in the form x y + y x {displaystyle x^{y}+y^{x}} and x y − y x {displaystyle x^{y}-y^{x}} , and, as such, it is a Leyland prime and Leyland prime of the second kind:[6][7]
17 = 2 3 + 3 2 = 3 4 − 4 3 {displaystyle 17=2^{3}+3^{2}=3^{4}-4^{3}}
17 is one of seven lucky numbers of Euler which produce primes of the form k 2 − k + 41 {displaystyle k^{2}-k+41} .[8]
Seventeen is the sixth Mersenne prime exponent, yielding 131,071.[9]
Seventeen is the third Fermat prime, as it is of the form 2 2 n + 1 {displaystyle 2^{2^{n}}+1} , specifically with n = 2 {displaystyle n=2} .[10] Since 17 is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss and ultimately led him to choose mathematics over philology for his studies.[11][12]
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".[13]
Seventeen is the minimum number of vertices on a graph such that, if the edges are coloured with three different colours, there is bound to be a monochromatic triangle; see Ramsey's theorem.[14]
There are also:
17 crystallographic space groups in two dimensions.[15] These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.
17 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the three-variable Laplace equation can be solved using the separation of variables technique.
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17 four-dimensional parallelotopes that are zonotopes. Another 34, or twice 17, are Minkowski sums of zonotopes with the 24-cell, itself the simplest parallelotope that is not a zonotope.[26]
Seventeen is the highest dimension for paracompact Vinberg polytopes with rank n + 2 {displaystyle n+2} mirror facets, with the lowest belonging to the third.[27]
Seventeen is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved between 2012 and 2014.[28][29]
The sequence of residues (mod n) of a googol and googolplex, for n = 1 , 2 , 3 , . . . {displaystyle n=1,2,3,...} , agree up until n = 17 {displaystyle n=17} .
A positive definite quadratic integer matrix represents all primes when it contains at least the set of 17 numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}.[30] Only four prime numbers up to 73 are not part of the set.
In science [ edit ]
In languages [ edit ]
Grammar [ edit ]
In Catalan, 17 is the first compound number (disset). The numbers 11 (onze) through 16 (setze) have their own names.
In French, 17 is the first compound number (dix-sept). The numbers 11 (onze) through 16 (seize) have their own names.
In Italian, 17 is also the first compound number (diciassette), whereas sixteen is sedici.
Age 17 [ edit ]
In culture [ edit ]
Music [ edit ]
Bands [ edit ]
17 Hippies, a German band
Seventeen ( 세븐틴 ), a South Korean boy band
), a South Korean boy band Heaven 17, an English new wave band
East 17, an English boy band
Albums [ edit ]
Songs [ edit ]
Other [ edit ]
Seventeen , a 1951 American musical
, a 1951 American musical The ratio 18:17 was a popular approximation for the equal tempered semitone during the Renaissance
Film [ edit ]
Anime and manga [ edit ]
Android 17, a character from the Dragon Ball series
series Detective Konawaka from the Paprika anime has a strong dislike for the number 17
Games [ edit ]
The computer game Half-Life 2 takes place in and around City 17
takes place in and around City 17 The visual novel Ever 17: The Out of Infinity strongly revolves around the number 17
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, a magazine The title of Just Seventeen , a former magazine
, 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".
, 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 [ edit ]
According to Plutarch's Moralia, the Egyptians have a legend that the end of Osiris' life came on the seventeenth of a month, on which day it is quite evident to the eye that the period of the full moon is over. Now, because of this, the Pythagoreans call this day "the Barrier", and utterly abominate this number. For the number seventeen, coming in between the square sixteen and the oblong rectangle eighteen, which, as it happens, are the only plane figures that have their perimeters equal their areas, bars them off from each other and disjoins them, and breaks up the epogdoon by its division into unequal intervals. [34]
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 Salat on a daily basis.
Wager Mage
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