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20000
20,000 (twenty thousand) is the natural number that comes after 19,999 and before 20,001. 20,000 is a round number, and is also in the title of Jules Verne's novel ''Twenty Thousand Leagues Under the Sea''. Selected numbers in the range 20001–29999 20001 to 20999 * 20002 = number of surface-points of a tetrahedron with edge-length 100 * 20100 = sum of the first 200 natural numbers (hence a triangular number) * 20160 = highly composite number; the smallest order belonging to two non-isomorphic simple groups: the alternating group ''A''8 and the Chevalley group ''A''2(4) * 20161 = the largest integer that cannot be expressed as a sum of two abundant numbers * 20230 = pentagonal pyramidal number * 20412 = Leyland number: 93 + 39 * 20540 = square pyramidal number * 20569 = tetranacci number * 20593 = unique prime in base 12 * 20597 = k such that the sum of the squares of the first k primes is divisible by k. * 20736 = 1442 = 124, 10000Duodecimal, 12, Palindromic number, palindromic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jules Verne
Jules Gabriel Verne (;''Longman Pronunciation Dictionary''. ; 8 February 1828 – 24 March 1905) was a French novelist, poet, and playwright. His collaboration with the publisher Pierre-Jules Hetzel led to the creation of the ''Voyages extraordinaires'', a series of bestselling adventure novels including ''Journey to the Center of the Earth'' (1864), ''Twenty Thousand Leagues Under the Seas'' (1870), and '' Around the World in Eighty Days'' (1872). His novels, always well documented, are generally set in the second half of the 19th century, taking into account the technological advances of the time. In addition to his novels, he wrote numerous plays, short stories, autobiographical accounts, poetry, songs and scientific, artistic and literary studies. His work has been adapted for film and television since the beginning of cinema, as well as for comic books, theater, opera, music and video games. Verne is considered to be an important author in France and most of Europe, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twenty Thousand Leagues Under The Sea
''Twenty Thousand Leagues Under the Seas'' (french: Vingt mille lieues sous les mers) is a classic science fiction adventure novel by French writer Jules Verne. The novel was originally serialized from March 1869 through June 1870 in Pierre-Jules Hetzel's fortnightly periodical, the . A deluxe octavo edition, published by Hetzel in November 1871, included 111 illustrations by Alphonse de Neuville and Édouard Riou. The book was widely acclaimed on its release and remains so; it is regarded as one of the premier adventure novels and one of Verne's greatest works, along with '' Around the World in Eighty Days'' and ''Journey to the Center of the Earth''. Its depiction of Captain Nemo's underwater ship, the ''Nautilus'', is regarded as ahead of its time, since it accurately describes many features of today's submarines, which in the 1860s were comparatively primitive vessels. A model of the French submarine ''Plongeur'' (launched in 1863) figured at the 1867 Exposition Universe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unique Prime
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737. Like all rational numbers, the reciprocals of primes have repeating decimal representations. In his later years, George Salmon (1819–1904) concerned himself with the repeating periods of these decimal representations of reciprocals of primes. Contemporaneously, William Shanks (1812–1882) calculated numerous reciprocals of primes and their repeating periods, and published two papers "On Periods in the Reciprocals of Primes" in 1873 and 1874. In 1874 he also published a table of primes, and the periods of their reciprocals, up to 20,000 (with help from and "communicated by the Rev. George Salmon"), and pointed out the errors in previous tables by three other authors. Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. For a prime , the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seventeen Or Bust
Seventeen or Bust was a volunteer computing project started in March 2002 to solve the last seventeen cases in the Sierpinski problem. The project solved eleven cases before a server loss in April 2016 forced it to cease operations. Work on the Sierpinski problem moved to PrimeGrid, which solved a twelfth case in October 2016. Five cases remain unsolved . Goals The goal of the project was to prove that 78557 is the smallest Sierpinski number, that is, the least odd ''k'' such that ''k''·2''n''+1 is composite (i.e. not prime) for all ''n'' > 0. When the project began, there were only seventeen values of ''k'' 0 (or else ''k'' has algebraic factorizations for some ''n'' values and a finite prime set that works only for the remaining ''n''). For example, for the smallest known Sierpinski number, 78557, the covering set is . For another known Sierpinski number, 271129, the covering set is . Each of the remaining sequences has been tested and none has a small cove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...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] |
Full Reptend Prime
In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat quotient : q_p(b) = \frac (where ''p'' does not divide ''b'') gives a cyclic number. Therefore, the base ''b'' expansion of 1/p repeats the digits of the corresponding cyclic number infinitely, as does that of a/p with rotation of the digits for any ''a'' between 1 and ''p'' − 1. The cyclic number corresponding to prime ''p'' will possess ''p'' − 1 digits if and only if ''p'' is a full reptend prime. That is, the multiplicative order = ''p'' − 1, which is equivalent to ''b'' being a primitive root modulo ''p''. The term "long prime" was used by John Conway and Richard Guy in their ''Book of Numbers''. Confusingly, Sloane's OEIS refers to these primes as "cyclic numbers". Base 10 Base 10 may be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s. The Bell numbers are denoted B_n, where n is an integer greater than or equal to zero. Starting with B_0 = B_1 = 1, the first few Bell numbers are :1, 1, 2, 5, 15, 52, 203, 877, 4140, ... . The Bell number B_n counts the number of different ways to partition a set that has exactly n elements, or equivalently, the number of equivalence relations on it. B_n also counts the number of different rhyme schemes for n -line poems. As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, B_n is the n -th moment of a Poisson distribution with mean 1. Counting Set partitions In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary). Repdigits are the representation in base B of the number x\frac where 0 1 and ''n'', ''m'' > 2 : **(''p'', ''x'', ''y'', ''m'', ''n'') = (31, 5, 2, 3, 5) corresponding to 31 = 111112 = 1115, and, **(''p'', ''x'', ''y'', ''m'', ''n'') = (8191, 90, 2, 3, 13) corresponding to 8191 = 11111111111112 = 11190, with 11111111111 is the repunit with thirteen digits 1. *For each sequence of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedral Number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ''n''th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral numbers are: : 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891 . Properties and applications The octahedral numbers have a generating function : \frac = \sum_^ O_n z^n = z +6z^2 + 19z^3 + \cdots . Sir Frederick Pollock conjectured in 1850 that every positive integer is the sum of at most 7 octahedral numbers. This statement, the Pollock octahedral numbers conjecture, has been proven true for all but finitely many numbers. In chemistry, octahedral numbers may be used to describe the numbers of atoms in octahedral clusters; in this context they are called magic numbers.. Relation to other figurate numbers Square pyramids An octahedral packing of spheres may be partitioned into two square pyramids, one upside-down underneath ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A0001003
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
