17 (number)

17 (disambiguation)17 yes November 2025 17 septendecimal prime 7th 1, 17 Hebrew numeral י"ז Babylonian numeral 𒌋𒐛 17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. Mathematics 17 is a Leyland numberA094133 Leyland numbers and Leyland prime,A094133 Leyland prime numbers using 2 and 3 (23 + 32),A045575 Leyland numbers of the second kindA123206 and using 3 and 4 (34 - 43). 17 is one of five known Fermat primes, and one of six total lucky numbers of Euler.A014556 Euler's "Lucky" numbers 25 November 2022 Since seventeen 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.Conway John H. The Book of Numbers The Book of Numbers (math book) Guy Richard K. Copernicus 1996 New York 11 Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compassesPappas Theoni Theoni Pappas Mathematical Snippets 2008 42 The minimum possible number of givens for a sudoku puzzle with a unique solution is 17.1201.0749 cs.DS Gary McGuire There is no 16-clue sudoku: solving the sudoku minimum number of clues problem 2012McGuire Gary Tugemann Bastian Civario Gilles 2014 There is no 16-clue sudoku: Solving the sudoku minimum number of clues problem via hitting set enumeration Experimental Mathematics 23 2 190–217 10.1080/10586458.2013.870056 8973439 Geometric properties Two-dimensions upright=1.45|right|thumb|The Spiral of Theodorus, with a maximum right triangles laid edge-to-edge before one revolution is completed. The largest triangle has a hypotenuse of There are seventeen crystallographic space groups in two dimensions.A006227 Number of n-dimensional space groups (including enantiomorphs) 25 November 2022 These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper. Also in two dimensions, seventeen is the number of combinations of regular polygons that completely fill a plane vertex.Dallas Elmslie William The Elements of Plane Practical Geometry, Etc 134 1855 https://books.google.com/books?id=y4BaAAAAcAAJ&pg=PA134 John W. Parker & Son. Eleven of these belong to regular and semiregular tilings, while 6 of these (3.7.42,Shield - a 3.7.42 tiling http://gruze.org/tilings/3_7_42_shield 7 March 2022 Kevin Jardine's projects Kevin Jardine 3.8.24,Dancer - a 3.8.24 tiling http://gruze.org/tilings/dancer 7 March 2022 Kevin Jardine's projects Kevin Jardine 3.9.18,Art - a 3.9.18 tiling http://gruze.org/tilings/3_9_18_art 7 March 2022 Kevin Jardine's projects Kevin Jardine 3.10.15,Fighters - a 3.10.15 tiling http://gruze.org/tilings/3_10_15_fighters 7 March 2022 Kevin Jardine's projects Kevin Jardine 4.5.20,Compass - a 4.5.20 tiling http://gruze.org/tilings/compass 7 March 2022 Kevin Jardine's projects Kevin Jardine and 5.5.10)Broken roses - three 5.5.10 tilings http://gruze.org/tilings/5_5_10_broken_roses 7 March 2022 Kevin Jardine's projects Kevin Jardine exclusively surround a point in the plane and fill it only when irregular polygons are included.Pentagon-Decagon Packing https://blogs.ams.org/visualinsight/2015/02/01/pentagon-decagon-packing/ 7 March 2022 American Mathematical Society AMS Seventeen is the minimum number of vertices on a two-dimensional graph such that, if the edges are colored with three different colors, there is bound to be a monochromatic triangle; see Ramsey's theorem.A003323 Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's. 25 November 2022 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".Babbitt Frank Cole https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html#42 Plutarch's Moralia Loeb 1936 V 17 is the least for the Theodorus Spiral to complete one revolution.A072895 Least k for the Theodorus spiral to complete n revolutions 19 June 2024 This, in the sense of Plato, who questioned why Theodorus (his tutor) stopped at when illustrating adjacent right triangles whose bases are units and heights are successive square roots, starting with . In part due to Theodorus's work as outlined in Plato's Theaetetus, it is believed that Theodorus had proved all the square roots of non-square integers from 3 to 17 are irrational by means of this spiral. Enumeration of icosahedron stellations In three-dimensional space, there are seventeen distinct fully supported stellations generated by an icosahedron.Webb Robert Enumeration of Stellations https://www.software3d.com/Enumerate.php https://archive.today/20221126015207/https://www.software3d.com/Enumerate.php 26 November 2022 25 November 2022 www.software3d.com The seventeenth prime number is 59, which is equal to the total number of stellations of the icosahedron by Miller's rules.Coxeter H. S. M. Harold Scott MacDonald Coxeter The Fifty-Nine Icosahedra Du Val P. Flather H. T. Petrie J. F. Springer 1982 978-1-4613-8216-4 New York 10.1007/978-1-4613-8216-4A000040 The prime numbers 17 February 2023 Without counting the icosahedron as a zeroth stellation, this total becomes 58, a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17).A007504 Sum of the first n primes. 17 February 2023 Seventeen distinct fully supported stellations are also produced by truncated cube and truncated octahedron. Four-dimensional zonotopes Seventeen is also the number of 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.Senechal Marjorie Marjorie Senechal Galiulin R. V. 1984 An introduction to the theory of figures: the geometry of E. S. Fedorov Structural Topology en,fr 10 5–22 2099/1195 768703 Abstract algebra Seventeen is the highest dimension for paracompact Vineberg polytopes with rank mirror facets, with the lowest belonging to the third.Tumarkin P.V. May 2004 Hyperbolic Coxeter N-Polytopes with n+2 Facets https://doi.org/10.1023/B:MATN.0000030993.74338.dd Mathematical Notes 75 5/6 848–854 math/0301133 10.1023/B:MATN.0000030993.74338.dd 18 March 2022 17 is a supersingular prime, because it divides the order of the Monster group.A002267 The 15 supersingular primes 25 November 2022 If the Tits group is included as a non-strict group of Lie type, then there are seventeen total classes of Lie groups that are simultaneously finite and simple (see classification of finite simple groups). In base ten, (17, 71) form the seventh permutation class of permutable primes.A258706 Absolute primes: every permutation of digits is a prime. Only the smallest representative of each permutation class is shown. 29 June 2023 Other interesting properties The sequence of residues (mod n) of a googol and googolplex, for , agree up until .August 2024 A series of length seventeen is the longest sequence for which a solution exists in the irregularity of distributions problem.Berlekamp, E. R. Graham, R. L. 1970 Irregularities in the distributions of finite sequences Journal of Number Theory 2 2 152–161 1970JNT.....2..152B 10.1016/0022-314X(70)90015-6 0269605 free right|240px|thumb|There are seventeen elementary particles in the Standard Model of physics. Other fields Poetry 17 is the number of syllables in a traditional Japanese haiku, arranged in 3 lines of 5, 7, and 5 syllables. Psychology 17 was described at MIT as "the least random number", according to the Jargon File.random numbers http://www.catb.org/~esr/jargon/html/R/random-numbers.html catb.org/ 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 Power of 17 http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/ dead https://web.archive.org/web/20081204111153/http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/ 4 December 2008 14 June 2010 Cosmic VarianceThe current source is insufficiently reliable (WP:NOTRS). September 2026 References Berlekamp, E. R. Elwyn Berlekamp Graham, R. L. Ronald L. Graham 1970 Irregularities in the distributions of finite sequences Journal of Number Theory 2 2 152–161 1970JNT.....2..152B 10.1016/0022-314X(70)90015-6 0269605 free External links seventeen Prime Curios!: 17 Is 17 the "most random" number? zero Category:Integers Category:Prime numbers