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5000 (number)
5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is, at the same time, the largest isogrammic numeral, and the smallest number that contains every one of the five vowels (a, e, i, o, u) in certain dialects of the English language (i.e. those that do not include the word “and” when writing out 230, 250, 260, 602, and 640). 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 * 5077 – prime of the form 2p-1 * 5081 – Sophie Germain prime * 5087 – safe prime * 5099 – safe prime 5100 to 5199 * 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armenian Numerals
Armenian numerals form a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet. There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the ancient Greek numerals and Hebrew numerals. In modern Armenia, the familiar Arabic numerals are used. In contemporary writing, Armenian numerals are used more or less like Roman numerals in modern English, e.g. Գարեգին Բ. means Garegin II and Գ. գլուխ means ''Chapter III'' (as a headline). The final two letters of the Armenian alphabet, "o" (Օ) and "fe" (Ֆ), were added to the Armenian alphabet only after Arabic numerals were already in use, to facilitate transliteration of other languages. Thus, they sometimes have a numerical value assigned to them. Notation As in Hebrew and ancient notation, in Armenian numerals distinct symbols represent multiples of po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balanced Prime
In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, the nth prime number p_n is a balanced prime if :p_n = . For example, 53 is the sixteenth prime; the fifteenth and seventeenth primes, 47 and 59, add up to 106, and half of that is 53; thus 53 is a balanced prime. Examples The first few balanced primes are 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903 . Infinitude It is conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...d that there are infinitely many balanced primes. Three consecutive primes in arithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegner Number
In number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ..., 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, the ring of algebraic integers of \Q\left sqrt\right/math> 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 that the gap in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
J-invariant
In mathematics, Felix Klein's -invariant or function is a modular function of weight zero for the special linear group \operatorname(2,\Z) defined on the upper half-plane of complex numbers. It is the unique such function that is holomorphic away from a simple pole at the cusp such that :j\big(e^\big) = 0, \quad j(i) = 1728 = 12^3. Rational functions of j are modular, and in fact give all modular functions of weight 0. Classically, the j-invariant was studied as a parameterization of elliptic curves over \mathbb, 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 \mathcal=\, by :j(\tau) = 1728 \frac = 1728 \frac = 1728 \frac with the third definition implying j(\tau) can be expressed as a cube, also since 1728 = 12^3. The function cannot be continued analytically beyond the upper half-plane due to the natura ... [...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. In British imperial and US customary units, it is defined as feet, equal to exactly of a mile, or yards (a quarter of a surveyor's chain), and is exactly 5.0292 meters. The rod is useful as a unit of length because integer 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 (a chain) wide (220 yards by 22 yards) or, equivalently, 40 rods by 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 utilized in national armies. The tool has been supplanted, first by steel tapes and later by el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yard
The yard (symbol: yd) is an English units, English unit of length in both the British imperial units, imperial and US United States customary units, customary systems of measurement equalling 3 foot (unit), feet or 36 inches. Since 1959 it has been by international yard and pound, international agreement standardized as exactly 0.9144 Metre, meter. A distance of 1,760 yards is equal to 1 mile. The theoretical survey foot, 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 Ine of Wessex#Laws, laws of Ine of Wessex, wherein the "yard of land" mentioned is the virgate, yardland, an old English unit of tax assessment equal to hide (unit), 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merriam-Webster
Merriam-Webster, Incorporated is an list of companies of the United States by state, American company that publishes reference work, reference books and is mostly known for Webster's Dictionary, its dictionaries. It is the oldest dictionary publisher in the United States. In 1831, George Merriam, 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 ''Webster's Dictionary#Noah Webster's American Dictionary of the English Language, 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, Merriam-Webster, Incorporated, in 1982. History 19th century In 1806, Webster published his first dictionary, s:A Compendious Dictionary of the English Language, ''A Compen ... [...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 imperial unit, British imperial unit and United States customary unit of length; both are based on the older English unit of Unit of length, length equal to 5,280 Foot (unit), English feet, or 1,760 yards. The statute mile was standardised between the Commonwealth of Nations and the United States by an international yard and pound, 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, Roman mile (roughly ), such as the #Nautical, nautical mile (now exactly), the #Italian, Italian mile (roughly ), and the li (unit), Chinese mile (now exactly). The Romans divided their mile into 5,000 (), but the greater importance of furlongs in the Kingdom of England#Tudor period, Elizabethan-era England meant th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foot (unit)
The foot (standard symbol: ft) is a Units of measurement, unit of length in the imperial units, British imperial and United States customary units, United States customary systems of metrology, measurement. The prime (symbol), prime symbol, , is commonly used to represent the foot. In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since international yard and pound, an international agreement in 1959, the foot is defined as equal to exactly 0.3048 meters. Historically, the "foot" was a part of many local systems of units, including the Ancient Greek units of measurement, Greek, Ancient Roman units of measurement, Roman, Chinese units of measurement, Chinese, Units of measurement in France before the French Revolution, French, and English units, 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 ... [...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. 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 factorization becomes harder as the numbers get larger. Example The cototient of x is defined as x - \phi(x), i.e. the number of positive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonagonal Number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical. Specifically, the ''n''th nonagonal number counts the dots in a pattern of ''n'' nested nonagons, all sharing a common corner, where the ''i''th nonagon in the pattern has sides made of ''i'' dots spaced one unit apart from each other. The nonagonal number for ''n'' is given by the formula: :\frac . Nonagonal numbers The first few nonagonal numbers are: :0 (number), 0, 1 (number), 1, 9 (number), 9, 24 (number), 24, 46 (number), 46, 75 (number), 75, 111 (number), 111, 154 (number), 154, 204 (number), 204, 261 (number), 261, 325 (number), 325, 396 (number), 396, 474 (number), 474, 559 (number), 559, 651 (number), 651, 750 (number), 750, 856 (number), 856, 96 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Prime (recreational Mathematics)
In recreational number theory, a minimal prime is a prime number for which there is no shorter subsequence of its digits in a given base that form a prime. In base 10 there are exactly 26 minimal primes: : 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 . For example, 409 is a minimal prime because there is no prime among the shorter subsequences of the digits: 4, 0, 9, 40, 49, 09. The subsequence does not have to consist of consecutive digits, so 109 is not a minimal prime (because 19 is prime). But it does have to be in the same order; so, for example, 991 is still a minimal prime even though a subset of the digits can form the shorter prime 19 by changing the order. Similarly, there are exactly 32 composite numbers which have no shorter composite subsequence: :4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
