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113 (number)
113 (one hundred ndthirteen) is the natural number following 112 and preceding 114. Mathematics * 113 is the 30th prime number (following 109 and preceding 127), so it can only be divided by one and itself. 113 is a Sophie Germain prime, an emirp, an isolated prime, a Chen prime and a Proth prime as it is a prime number of the form 7 × 24 + 1. 113 is also an Eisenstein prime with no imaginary part and real part of the form 3n - 1. In base 10, this prime is a primeval number, and a permutable prime with 131 and 311. *113 is a highly cototient number and a centered square number. *113 is the denominator of 355/113, an accurate approximation to . See also * 113 (other) * A113 is A Pixar recurring inside joke or Easter Egg, e.g.: (WALL-E) = (W-A113). References * Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutable Prime
A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to study these primes, called them permutable primes, but later they were also called absolute primes. In base 10, all the permutable primes with fewer than 49,081 digits are known : 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, R19 (1111111111111111111), R23, R317, R1031, ... Of the above, there are 16 unique permutation sets, with smallest elements :2, 3, 5, 7, R2, 13, 17, 37, 79, 113, 199, 337, R19, R23, R317, R1031, ... Note R''n'' = \tfrac is a repunit, a number consisting only of ''n'' ones (in base 10). Any repunit prime is a permutable prime with the above definition, but some definitions require at least two distinct digits. All permutable primes of two or more digits are comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WALL-E
''WALL-E'' (stylized with an interpunct as ''WALL·E'') is a 2008 American computer-animated science fiction film produced by Pixar Animation Studios and released by Walt Disney Pictures. It was directed and co-written by Andrew Stanton, produced by Jim Morris, and co-written by Jim Reardon. It stars the voices of Ben Burtt, Elissa Knight, Jeff Garlin, John Ratzenberger, Kathy Najimy, with Sigourney Weaver and Fred Willard. The overall ninth feature film produced by the studio, ''WALL-E'' follows a solitary robot on a future, uninhabitable, deserted Earth in 2805, left to clean up garbage. He is visited by a probe sent by the starship ''Axiom'', a robot called EVE, with whom he falls in love and pursues across the galaxy. After directing ''Finding Nemo'', Stanton felt Pixar had created believable simulations of underwater physics and was willing to direct a film set largely in space. ''WALL-E'' has minimal dialogue in its early sequences; many of the characters do not have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A113
A113 (sometimes A-113, A-1-13, A1-13 or A11-3) is an inside joke and Easter egg in media developed by alumni of California Institute of the Arts, referring to the classroom used by graphic design and character animation students. History Students who have used the classroom include John Lasseter, Tim Burton, Michael Peraza, and Brad Bird. It has appeared in other Disney movies and almost every Pixar movie. Brad Bird first used it for a license plate number in the " Family Dog" episode of ''Amazing Stories'': "I put it into every single one of my films, including my ''Simpsons'' episodes—it's sort of my version of caricaturist Al Hirschfeld's 'Nina'." It appears in South Park, Aqua Teen Hunger Force and the SPA Studios animated film Klaus. See also * List of Pixar film references * List of filmmaker's signatures * 42 – ''The Answer to Life, the Universe, and Everything'', first used by Douglas Adams in ''The Hitchhiker's Guide to the Galaxy ''The Hitchhiker's Guid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
113 (other) , synthetic chemical element with atomic number 113
{{Numberdis ...
113 may refer to: *113 (number), a natural number *AD 113, a year *113 BC, a year *113 (band), a French hip hop group *113 (MBTA bus), Massachusetts Bay Transportation Authority bus route *113 (New Jersey bus), Ironbound Garage in Newark and run to and from the Port Authority bus route See also * 11/3 (other) *Nihonium Nihonium is a synthetic chemical element with the symbol Nh and atomic number 113. It is extremely radioactive; its most stable known isotope, nihonium-286, has a half-life of about 10 seconds. In the periodic table, nihonium is a transactinid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milü
Milü (; "close ratio"), also known as Zulü ( Zu's ratio), is the name given to an approximation to (pi) found by Chinese mathematician and astronomer Zu Chongzhi in the 5th century. Using Liu Hui's algorithm (which is based on the areas of regular polygons approximating a circle), Zu famously computed to be between 3.1415926 and 3.1415927 and gave two rational approximations of , and , naming them respectively Yuelü (; "approximate ratio") and Milü. is the best rational approximation of with a denominator of four digits or fewer, being accurate to six decimal places. It is within % of the value of , or in terms of common fractions overestimates by less than . The next rational number (ordered by size of denominator) that is a better rational approximation of is , still only correct to six decimal places and hardly closer to than . To be accurate to seven decimal places, one needs to go as far as . For eight, is needed. The accuracy of Milü to the true value of ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denominator
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: \tfrac and \tfrac) consists of a numerator, displayed above a line (or before a slash like ), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not ''common'', including compound fractions, complex fractions, and mixed numerals. In positive common fractions, the numerator and denominator are natural numbers. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero, because zero parts can never make up a whole. For example, in the fraction , the numerator 3 indicates that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Square Number
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any direct practical applications, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties. The figures for the first four centered square numbers are shown below: : Each centered square number is the sum of successive squares. Example: as shown in the following figure of Floyd's triangle, 25 is a centered square number, and is the sum of the square 16 (yellow rhombus formed by shearing a square) and of the next smaller square, 9 (sum of two blue triangles): Relationships with o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highly Cototient Number
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient function. There are infinitely many solutions to the equation for :k = 1 so this value is excluded in the definition. The first few highly cototient numbers are: : 2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889, ... Many of the highly cototient numbers are odd. In fact, after 8, all the numbers listed above are odd, and after 167 all the numbers listed above are congruent to 29 modulo 30. The concept is somewhat analogous to that of highly composite numbers. Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers. Computations become harder, since integer factori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
311 (number)
311 (three hundred ndeleven) is the natural number following 310 and preceding 312. In mathematics 311 is the 64th prime; a twin prime with 313; an irregular prime; an emirp, an Eisenstein prime with no imaginary part and real part of the form 3n - 1; a Gaussian prime with no imaginary part and real part of the form 4n - 1; and a permutable prime with 113 and 131. It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). 311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309. 311 is the smallest positive integer ''d'' such that the imaginary quadratic field Q() has class number = 19. Notable uses of numerical value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
131 (number)
131 (one hundred [and] thirty-one) is the natural number following 130 (number), 130 and preceding 132 (number), 132. In mathematics 131 is a Sophie Germain prime, an irregular prime, the second 3-digit palindromic prime, and also a permutable prime with 113 (number), 113 and 311 (number), 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an Eisenstein prime with no imaginary part and real part of the form 3n - 1. Because the next odd number, 133, is a semiprime, 131 is a Chen prime. 131 is an Ulam number. 131 is a full reptend prime in base (exponentiation), base 10 (and also in base 2). The decimal expansion of 1/131 repeats the digits 007633587786259541984732824427480916030534351145038167938931 297709923664122137404580152671755725190839694656488549618320 6106870229 indefinitely. In the military * Convair C-131 Samaritan was an American military transport produced from 1954 in aviation, 1954 to 1956 in aviation, 1956 * VFA-131, Strike Fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primeval Number
In recreational number theory, a primeval number is a natural number ''n'' for which the number of prime numbers which can be obtained by permuting some or all of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith. The first few primeval numbers are :1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, ... The number of primes that can be obtained from the primeval numbers is :0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, 31, 33, 35, 41, 53, 55, 60, 64, 89, 96, 106, ... The largest number of primes that can be obtained from a primeval number with ''n'' digits is :1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505, ... The smallest ''n''-digit number to achieve this number of primes is :2, 37, 137, 1379, 13679, 123479, 1234679, 12345679, 102345679, 1123456789, 10123456789, .. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
