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6000 (number)
6000 (six thousand) is the natural number following 5999 and preceding 6001. Selected numbers in the range 6001–6999 6001 to 6099 * 6025 – Rhythm guitarist of the Dead Kennedys from June 1978 to March 1979. Full name is Carlos Cadona. * 6028 – centered heptagonal number * 6037 – super-prime, prime of the form 2p-1 * 6047 – safe prime * 6053 – Sophie Germain prime * 6069 – nonagonal number * 6073 – balanced prime * 6079 – The serial number Winston Smith is referred to as in the George Orwell novel ''Nineteen Eighty-Four'' * 6084 = 782, sum of the cubes of the first twelve integers * 6089 – highly cototient number * 6095 – magic constant of ''n'' × ''n'' normal magic square and n-Queens Problem for ''n'' = 23. 6100 to 6199 * 6101 – Sophie Germain prime * 6105 – triangular number * 6113 – Sophie Germain prime, super-prime * 6121 – prime of the form 2p-1 * 6131 – Sophie Germain prime, twin prime with 6133 * 6133 – 800th prime number, tw ... [...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] |
Thabit Number
In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 \cdot 2^n - 1 for a non-negative integer ''n''. The first few Thabit numbers are: : 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ... The 9th century mathematician, physician, astronomer and translator Thābit ibn Qurra is credited as the first to study these numbers and their relation to amicable numbers. Properties The binary representation of the Thabit number 3·2''n''−1 is ''n''+2 digits long, consisting of "10" followed by ''n'' 1s. The first few Thabit numbers that are prime (Thabit primes or 321 primes): :2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, ... , there are 66 known prime Thabit numbers. Their ''n'' values are: :0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Pyramidal Number
A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to pyramids with three or more sides. The numbers of points in the base (and in parallel layers to the base) are given by polygonal numbers of the given number of sides, while the numbers of points in each triangular side is given by a triangular number. It is possible to extend the pyramidal numbers to higher dimensions. Formula The formula for the th -gonal pyramidal number is :P_n^r= \frac, where , . This formula can be factored: :P_n^r=\frac=\left(\frac\right)\left(\frac\right)=T_n \cdot \frac, where is the th triangular number. Sequences The first few triangular pyramidal numbers (equivalently, tetrahedral numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rashad Khalifa
Rashad Khalifa ( ar, رشاد خليفة; November 19, 1935 – January 31, 1990) was an Egyptian-American biochemist, closely associated with the United Submitters International (USI), an organization which promotes the practice and study of Quran-only Islam. His teachings were opposed by Traditionalist Muslims and he was assassinated on January 31, 1990. He is also known for his claims regarding the existence of a Quran code, also known as Code 19. Life Khalifa was born in Egypt on November 19, 1935. He obtained an honors degree from Ain Shams University, Egypt, before he emigrated to the United States in 1959. He later earned a Master's Degree in biochemistry from University of Arizona and a Ph.D. from University of California, Riverside. He became a naturalized U.S. citizen and lived in Tucson, Arizona. He was married to an American woman and they had a son and a daughter together. Khalifa worked as a science adviser for the Libyan government for about one year, after whic ... [...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] |
Leyland Number
In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 . The requirement that ''x'' and ''y'' both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form ''x''1 + 1''x''. Also, because of the commutative property of addition, the condition ''x'' ≥ ''y'' is usually added to avoid double-covering the set of Leyland numbers (so we have 1 References External links * {{DEFAULTSORT:Leyland Number Integer sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Octagonal Number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the odd square numbers. Thus, the ''n''th odd square number and ''t''th centered octagonal number is given by the formula :O_n=(2n-1)^2 = 4n^2-4n+1 , (2t+1)^2=4t^2+4t+1. The first few centered octagonal numbers are : 1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225 Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number. O_n is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their permanent. See also * Octagonal number An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qur'an
The Quran (, ; Standard Arabic: , Quranic Arabic: , , 'the recitation'), also romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a revelation from God. It is organized in 114 chapters (pl.: , sing.: ), which consist of verses (pl.: , sing.: , cons.: ). In addition to its religious significance, it is widely regarded as the finest work in Arabic literature, and has significantly influenced the Arabic language. Muslims believe that the Quran was orally revealed by God to the final prophet, Muhammad, through the archangel Gabriel incrementally over a period of some 23 years, beginning in the month of Ramadan, when Muhammad was 40; and concluding in 632, the year of his death. Muslims regard the Quran as Muhammad's most important miracle; a proof of his prophethood; and the culmination of a series of divine messages starting with those revealed to Adam, including the Torah, the Psalms and the Gospel. The word ''Quran'' occurs so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amicable Number
Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, σ(''a'')=''b'' and σ(''b'')=''a'', where σ(''n'') is equal to the sum of positive divisors of ''n'' (see also divisor function). The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992). . (Also see and ) It is unknown if there are infinitely many pairs of amicable numbers. A pair of amic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuban Prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''. First series This is the first of these equations: :p = \frac,\ x = y + 1,\ y>0, i.e. the difference between two successive cubes. The first few cuban primes from this equation are : 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227 The formula for a general cuban prime of this kind can be simplified to 3y^2 + 3y + 1. This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal. the largest known has 65537 digits with y = 100000845^, found by Jens Kruse Andersen. Second series The second of these equations is: :p = \frac,\ x = y + 2,\ y>0. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Pyramidal Number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes. As well as counting spheres in a pyramid, these numbers can be described algebraically as a sum of the first n positive square numbers, or as the values of a cubic polynomial. They can be used to solve several other counting problems, including counting squares in a square grid and counting acute triangles formed from the vertices of an odd regular polygon. They equal the sums of consecutive tetrahedral numbers, and are one-fourth of a larger tetrahedral number. The sum of two consecutive square pyramidal numbers is an octahedral number. History The pyramidal numbers were one of the few types of three-dimensional figurate num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Divisor Number
In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: : 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 . Examples For example, the harmonic divisor number 6 has the four divisors 1, 2, 3, and 6. Their harmonic mean is an integer: : \frac=2. The number 140 has divisors 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Their harmonic mean is: : \frac=5 5 is an integer, making 140 a harmonic divisor number. Factorization of the harmonic mean The harmonic mean of the divisors of any number can be expressed as the formula :H(n) = \frac where is the sum of th powers of the divisors of : is the number of divisors, and is the sum of divisors . All of the terms in this formula are multiplicative, but not completely multiplicative. Therefore, the harmonic mean is also multiplicative. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
