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Cardinalseventeen
Ordinal17th
(seventeenth)
Numeral systemseptendecimal
Factorizationprime
Divisors1, 17
Roman numeralXVII
Binary10001
Octal21
Duodecimal15
Hexadecimal11

17 (seventeen) is the natural number following 16 and preceding 18. 18 ( eighteen) is the Natural number following 17 and preceding 19. In mathematics Nine is a Composite number, its proper Divisors being 1 and 3. 18 ( eighteen) is the Natural number following 17 and preceding 19. 19 ( nineteen) is the Natural number following 18 and preceding 20. "Twenty" redirects here For the village in England, see Twenty Lincolnshire. This is a list of articles about Numbers ( not about Numerals. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French "Twenty" redirects here For the village in England, see Twenty Lincolnshire. 30 ( thirty) is the Natural number following 29 and preceding 31. 40 ( forty) is the Natural number following 39 and preceding 41. This article discusses the number fifty. For the year 50 CE see 50. 60 ( sixty) is the Natural number following 59 and preceding 61. 70 ( seventy) is the Natural number following 69 and preceding 71. 80 ( eighty) is the Natural number following 79 and preceding 81. 90 ( ninety) is the Natural number preceded by 89 and followed by 91. This article describes cardinal numbers in mathematics For cardinals in linguistics see Names of numbers in English. In linguistics ordinal numbers are the words representing the rank of a number with respect to some order in particular order or position (i A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner In Mathematics, factorization ( also factorisation in British English) or factoring is the decomposition of an object (for In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 In Mathematics, a divisor of an Integer n, also called a factor of n, is an integer which evenly divides n without Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. The octal Numeral system, or oct for short is the base -8 number system and uses the digits 0 to 7 The duodecimal system (also known as base -12 or dozenal) is a Numeral system using twelve as its base. In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an 18 ( eighteen) is the Natural number following 17 and preceding 19. In English, it is the smallest number with nine letters when spelled out. English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States

Contents

In mathematics

Seventeen is the 7th prime number. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 The next prime is nineteen, with which it forms a twin prime. 19 ( nineteen) is the Natural number following 18 and preceding 20. A twin prime is a Prime number that differs from another prime number by Two. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071. In Mathematics, a Mersenne number is a positive integer that is one less than a Power of two: M_n=2^n-1 17 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. In Mathematics, an Eisenstein prime is an Eisenstein integer z = a + b\\omega\qquad(\omega = e^{2\pi i/3} that is irreducible

17 is the third Fermat prime, as it is of the form 2^{2^2} + 1, and it is also a Proth prime. In Mathematics, a Fermat number, named after Pierre de Fermat who first studied them is a positive integer of the form F_{n} = 2^{2^{ In Number theory, a Proth number is a number of the form P=k\ 2^n+1 where k is odd, n is a positive Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. Heptadecagon construction The regular heptadecagon is a Constructible polygon, as was shown by Carl Friedrich Gauss in 1796 A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists A ruler, or rule, is an instrument used in Geometry, Technical drawing and engineering/building to measure distances and/or to rule straight This was proven by Carl Friedrich Gauss. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German [1] Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes. A Higgs prime is a Prime number with a totient (one less than the prime that evenly divides the square of the product of the smaller Higgs primes

17 is the only positive Genocchi number that is prime, the only negative one being -3. The Genocchi numbers, named after Angelo Genocchi, are a sequence of Integers G n that satisfy the relation It is also the third Stern prime. A Stern prime, named for Moritz Abraham Stern, is a Prime number that is not the sum of a smaller prime and twice the square of a nonzero Integer

As 17 is the least prime factor of the first twelve terms of the Euclid-Mullin sequence, it is the thirteenth term. The Euclid-Mullin sequence is an infinite sequence of distinct Prime numbers in which each element is the least Prime factor of one plus the product of all earlier

There are exactly seventeen two-dimensional space (plane symmetry) groups. In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper. A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern based on the This page refers to the material used for Interior decoration.

Like 41, the number 17 is a prime that yields primes in the polynomial n2 + n + p, for all positive n < p - 1. 41 ( forty-one) is the Natural number following 40 and preceding 42. In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations

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. In Mathematics, the real numbers may be described informally in several different ways Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity In Mathematics, an interval is a set of Real numbers with the property that any number that lies between two numbers in the set is also included in the set The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).

16 and 18 unit squares can each be formed into rectangles with perimeter equal to the area; and they are the only solutions. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch explains that 17 is therefore an unlucky number. Platonism is the Philosophy of Plato or the name of other philosophical systems considered closely derived from it Lucius Mestrius Plutarchus ( Greek: Μέστριος Πλούταρχος c

17 is the tenth Perrin number, preceded in the sequence by 7, 10, 12. In Mathematics, the Perrin numbers are defined by the Recurrence relation P (0 = 3 P (1 = 0 P (2 = 2

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. William (Vilim Feller né Vilibald Srećko Feller ( July 7 1906 &ndash January 14 1970) was a Croatian American Princeton University is a private Coeducational research university located in Princeton, New Jersey. 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 was also known to use 17 as an arbitrary value during lectures. His Computational Mathematics Class would even include exactly 17 lectures.

17 is the least random number[2], according to the Hacker's Jargon File. The Jargon File is a Glossary of hacker Slang. The original Jargon File was a collection of hacker slang from technical cultures such as the MIT AI There is an unproved conjecture 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. Randomness is a lack of order Purpose, cause, or predictability [3]

17! = 355687428096000

It is a repunit prime in hexadecimal (11). In Recreational mathematics, a repunit is a Number like 11, 111, or 1111 that contains only the digit 1 In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a

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. is a Logic -based number-placement Puzzle. The objective is to fill a 9×9 grid so that each column each row and each of the nine 3×3 boxes (also called blocks

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. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point In Mathematics, Laplace's equation is a Partial differential equation named after Pierre-Simon Laplace who first studied its properties In Mathematics, separation of variables is any of several methods for solving ordinary and partial Differential equations in which algebra allows one to re-write an

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. 65 ( sixty-five) is the Natural number following 64 and preceding 66.

In science

Age 17

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In other fields

Seventeen is:

Historical years

A.D. 17, 17 B.C., 1917, 2017, etc. Year 17 was a Common year starting on Friday (link will display the full calendar of the Julian calendar. Year 17 BC was a Leap year starting on Friday (link will display the full calendar of the Julian calendar. Year 1917 ( MCMXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common year 2017 ( MMXVII) will be a Common year starting on Sunday of the Gregorian calendar.

References

  1. ^ John H. Conway and Richard K. Guy, The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777 - 1855) showed that the regular "heptadecagon" (a 17-sided polygon) could be constructed with ruler and compasses. "
  2. ^ "Random numbers"
  3. ^ Language Log: Another trip down Random Rd

External links

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