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17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. 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 vs 70 . 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 . 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 specifically with ''n'' = 2, and it is also a Proth prime. Since 17 is a Fermat prime, regular heptadecagons can be constructed with compass and unmarked ruler. This was proven by Carl Friedrich Gauss.〔John H. Conway and Richard K. Guy, ''The Book of Numbers''. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygon) could be constructed with ruler and compasses."〕 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. 17 is the average of the first two Perfect numbers. 17 is the thirteenth term of the Euclid–Mullin sequence. Seventeen is the aliquot sum of the semiprime , and is the aliquot sum of the semiprime , and is the base of the 17-aliquot tree. There are exactly 17 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 the least random number,〔("Random numbers" )〕 according to the Hackers' ''Jargon File.'' It is a repunit prime in hexadecimal (11). 17 is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved in 2012. 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. 17 is the minimum number of vertices on a graph such that, if the edges are coloured with 3 different colours, there is bound to be a monochromatic triangle. (See Ramsey's Theorem.) 17 is a full reptend prime in base 10, because its repeating decimal is 16 digits long. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「17 (number)」の詳細全文を読む スポンサード リンク
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