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2,000
2000 (two thousand) is a natural number following 1999 and preceding 2001. It is: :*the highest number expressible using only two unmodified characters in Roman numerals (MM) :*an Achilles number :*smallest four digit eban number Selected numbers in the range 2001–2999 2001 to 2099 * 2001 – sphenic number * 2002 – palindromic number * 2003 – Sophie Germain prime and the smallest prime number in the 2000s * 2004 – Area of the 24tcrystagon* 2005 – A vertically symmetric number * 2006 – number of subsets of with relatively prime elements * 2007 – 22007 + 20072 is prime * 2008 – number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to 3 * 2009 = 74 − 73 − 72 * 2010 – number of compositions of 12 into relatively prime parts * 2011 – Sexy prime with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 * 2012 – The number 8 × 102012 − 1 is a prime number * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ban Number
In recreational mathematics, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned." Ban numbers are not precisely defined, since some large numbers do not follow the standards of number names (such as googol and googolplex). There are several published sequences of ban numbers: * The aban numbers do not contain the letter A. The first few aban numbers are 1 through 999, 1,000,000 through 1,000,999, 2,000,000 through 2,000,999, ... The word "and" is not counted. * The eban numbers do not contain the letter E. The first few eban numbers are 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, 2000, 2002, 2004, ... . The sequence was coined in 1990 by Neil Sloane __NOTOC__ Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best know ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven: The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day. One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as: The notations and can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as "" on Roman numeral clocks. Other common uses include year numbers on monuments and buildings and ... [...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 Numbers
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] |
Mersenne Number
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Octahedral Number
A centered octahedral number or Haüy octahedral number is a figurate number that counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of the Delannoy numbers, which count certain two-dimensional lattice paths. The Haüy octahedral numbers are named after René Just Haüy. History The name "Haüy octahedral number" comes from the work of René Just Haüy, a French mineralogist active in the late 18th and early 19th centuries. His "Haüy construction" approximates an octahedron as a polycube, formed by accreting concentric layers of cubes onto a central cube. The centered octahedral numbers count the number of cubes used by this construction. Haüy proposed this construction, and several related constructions of other polyhedra, as a model for the structure of crystalline minerals.. See in particulapp. 13–14 As cited by Formula The number of three-dimensional lattice po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decagonal Number
A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal numbers are not rotationally symmetrical. Specifically, the ''n''th decagonal numbers counts the number of dots in a pattern of ''n'' nested decagons, all sharing a common corner, where the ''i''th decagon in the pattern has sides made of ''i'' dots spaced one unit apart from each other. The ''n''-th decagonal number is given by the following formula : D_n = 4n^2 - 3n. The first few decagonal numbers are: : 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326 The ''n''th decagonal number can also be calculated by adding the square of '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woodall Number
In number theory, a Woodall number (''W''''n'') is any natural number of the form :W_n = n \cdot 2^n - 1 for some natural number ''n''. The first few Woodall numbers are: :1, 7, 23, 63, 159, 383, 895, … . History Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly defined Cullen numbers. Woodall primes Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents ''n'' for which the corresponding Woodall numbers ''W''''n'' are prime are 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, ... ; the Woodall primes themselves begin with 7, 23, 383, 32212254719, ... . In 1976 Christopher Hooley showed that almost all Cullen numbers are composite. In October 1995, Wilfred Keller published a paper discussing several new Cullen primes and the efforts made to factorise other Cullen and Woodall numbers. Included in that paper is a personal communication to Kel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-Poulet Number
A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides :2''d'' − 2. For example, 341 is a super-Poulet number: it has positive divisors and we have: :(211 - 2) / 11 = 2046 / 11 = 186 :(231 - 2) / 31 = 2147483646 / 31 = 69273666 :(2341 - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When \frac is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number. The super-Poulet numbers below 10,000 are : Super-Poulet numbers with 3 or more distinct prime divisors It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors. Example: 2701 = 37 * 73 is a Poulet number, 4033 = 37 * 109 is a Poulet number, 7957 = 73 * 109 is a Poulet number; so 294409 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a Set (mathematics), set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of Comparability, comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Pentagonal Number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the formula :P_=, n\geq1 The first few centered pentagonal numbers are 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 . Properties *The parity of centered pentagonal numbers follows the pattern odd-even-even-odd, and in base 10 the units follow the pattern 1-6-6-1. *Centered pentagonal numbers follow the following Recurrence relations: :P_=P_+5n , P_0=1 :P_=3(P_-P_)+P_ , P_0=1,P_1=6,P_2=16 *Centered pentagonal numbers can be expressed using Triangular Numbers: :P_=5T_+1 See also *Pentagonal number *Polygonal number *Centered polygonal number The centered polygonal numbers are a class of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mian–Chowla Sequence
In mathematics, the Mian–Chowla sequence is an integer sequence defined recursion, recursively in the following way. The sequence starts with :a_1 = 1. Then for n>1, a_n is the smallest integer such that every pairwise sum :a_i + a_j is distinct, for all i and j less than or equal to n. Properties Initially, with a_1, there is only one pairwise sum, 1 + 1 = 2. The next term in the sequence, a_2, is 2 since the pairwise sums then are 2, 3 and 4, i.e., they are distinct. Then, a_3 can't be 3 because there would be the non-distinct pairwise sums 1 + 3 = 2 + 2 = 4. We find then that a_3 = 4, with the pairwise sums being 2, 3, 4, 5, 6 and 8. The sequence thus begins :1 (number), 1, 2 (number), 2, 4 (number), 4, 8 (number), 8, 13 (number), 13, 21 (number), 21, 31 (number), 31, 45 (number), 45, 66 (number), 66, 81 (number), 81, 97 (number), 97, 123 (number), 123, 148 (number), 148, 182 (number), 182, 204 (number), 204,252 (number), 252, 290 (number), 290, 361, 401, 475, ... . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
