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5050 (number)
5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the English language. Selected numbers in the range 5001–5999 5001 to 5099 * 5003 – Sophie Germain prime * 5020 – amicable number with 5564 * 5021 – super-prime, twin prime with 5023 * 5023 – twin prime with 5021 * 5039 – factorial prime, Sophie Germain prime * 5040 = 7!, superior highly composite number * 5041 = 712, centered octagonal number * 5050 – triangular number, Kaprekar number, sum of first 100 integers * 5051 – Sophie Germain prime * 5059 – super-prime * 5076 – decagonal number * 5081 – Sophie Germain prime * 5087 – safe prime * 5099 – safe prime 5100 to 5199 * 5107 – super-prime, balanced prime * 5113 – balanced prime * 5117 – sum of the first 50 primes * 5151 – triangular number * 5167 – Leonardo prime, cuban prime of the form ''x'' = ''y'' + 1 * 5171 – Sophie Germain prime * 5184 = 722 * 518 ... [...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] |
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] |
Magic Constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is (n^3+n)/2. The largest magic constant of normal magic square which is also a: *triangular number is 15 (solve the Diophantine equation x^2=y^3+16y+16, where y is divisible by 4); *square number is 1 (solve the Diophantine equation x^2=y^3+4y, where y is even); *generalized pentagonal number is 171535 (solve the Diophanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Kinkade
William Thomas Kinkade III (January 19, 1958 – April 6, 2012) was an American painter of popular realistic, pastoral, and idyllic subjects. He is notable for achieving success during his lifetime with the mass marketing of his work as printed reproductions and other licensed products by means of the Thomas Kinkade Company. According to Kinkade's company, one in every twenty American homes owned a copy of one of his paintings. Kinkade described himself as a "Painter of Light", a phrase he protected by trademark, but which was earlier used to describe the English artist J. M. W. Turner (1775–1851). Kinkade was criticized for some of his behavior and business practices; art critics faulted his work for being "kitsch". Kinkade died of "acute intoxication" from alcohol and the drug diazepam at the age of 54. Early life and education William Thomas Kinkade was born on January 19, 1958, in Sacramento County, California. He grew up in the town of Placerville, graduate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Number
In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factorization. The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–) Stark–Heegner theorem there are precisely nine Heegner numbers: This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated the gap in Heegner's proof was minor. Euler's prime-generating polynomial Euler's prime-generating polynomial n^2 + n + 41, which gives (distinct) primes for ''n'' = 0, ..., 39, is related to the Heegner number 163 = 4 · 41 − 1. Rabinowitz proved that n^2 + n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
J-invariant
In mathematics, Felix Klein's -invariant or function, regarded as a function of a Complex analysis, complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such function which is Holomorphic function, holomorphic away from a simple pole at the Cusp (singularity), cusp such that :j\left(e^\right) = 0, \quad j(i) = 1728 = 12^3. Rational functions of are modular, and in fact give all modular functions. Classically, the -invariant was studied as a parameterization of elliptic curves over , but it also has surprising connections to the symmetries of the Monster group (this connection is referred to as monstrous moonshine). Definition The -invariant can be defined as a function on the upper half-plane :j(\tau) = 1728 \frac = 1728 \frac = 1728 \frac with the third definition implying j(\tau) can be expressed as a Cube (algebra), cube, also since 1728 (number), 1728 = 12^3. The given functions are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rod (unit)
The rod, perch, or pole (sometimes also lug) is a surveyor's tool and unit of length of various historical definitions, often between approximately 3 and 8 meters (9 ft 10 in and 26 ft 2 in). In modern US customary units it is defined as US survey feet, equal to exactly of a surveyor's mile, or a quarter of a surveyor's chain ( yards), and is approximately 5.0292 meters. The rod is useful as a unit of length because whole number multiples of it can form one acre of square measure (area). The 'perfect acre' is a rectangular area of 43,560 square feet, bounded by sides 660 feet (a furlong) long and 66 feet wide (220 yards by 22 yards) or, equivalently, 40 rods and 4 rods. An acre is therefore 160 square rods or 10 square chains. The name ''perch'' derives from the Ancient Roman unit, the ''pertica''. The measure also has a relationship with the military pike of about the same size. Both measures date from the sixteenth century, when the pike was still ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yard
The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly 0.9144 meter. A distance of 1,760 yards is equal to 1 mile. The US survey yard is very slightly longer. Name The term, ''yard'' derives from the Old English , etc., which was used for branches, staves and measuring rods. It is first attested in the late 7th century laws of Ine of Wessex, where the "yard of land" mentioned is the yardland, an old English unit of tax assessment equal to hide. Around the same time the Lindisfarne Gospels account of the messengers from John the Baptist in the Gospel of Matthew used it for a branch swayed by the wind. In addition to the yardland, Old and Middle English both used their forms of "yard" to denote the surveying lengths of or , used in computing acres, a distance now usually known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merriam-Webster
Merriam-Webster, Inc. is an American company that publishes reference books and is especially known for its dictionaries. It is the oldest dictionary publisher in the United States. In 1831, George and Charles Merriam founded the company as G & C Merriam Co. in Springfield, Massachusetts. In 1843, after Noah Webster died, the company bought the rights to ''An American Dictionary of the English Language'' from Webster's estate. All Merriam-Webster dictionaries trace their lineage to this source. In 1964, Encyclopædia Britannica, Inc. acquired Merriam-Webster, Inc. as a subsidiary. The company adopted its current name in 1982. History Noah Webster In 1806, Webster published his first dictionary, ''A Compendious Dictionary of the English Language''. In 1807 Webster started two decades of intensive work to expand his publication into a fully comprehensive dictionary, ''An American Dictionary of the English Language''. To help him trace the etymology of words, Webster learned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mile
The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of distance; both are based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. The statute mile was standardised between the British Commonwealth and the United States by an international agreement in 1959, when it was formally redefined with respect to SI units as exactly . With qualifiers, ''mile'' is also used to describe or translate a wide range of units derived from or roughly equivalent to the Roman mile, such as the nautical mile (now exactly), the Italian mile (roughly ), and the Chinese mile (now exactly). The Romans divided their mile into 5,000 Roman feet but the greater importance of furlongs in Elizabethan-era England meant that the statute mile was made equivalent to or in 1593. This form of the mile then spread across the British Empire, some successor states of which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foot (unit)
The foot ( feet), standard symbol: ft, is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, , is a customarily used alternative symbol. Since the International Yard and Pound Agreement of 1959, one foot is defined as 0.3048 meters exactly. In both customary and imperial units, one foot comprises 12 inches and one yard comprises three feet. Historically the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits. The United States is the only industrialized nation that uses the international foot and the survey foot (a customary unit of length) in preference to the meter in its commercial, engin ... [...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] |
