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5500
5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is, at the same time, the largest Heterogram (literature), 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 (number), 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 * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Language
English is a West Germanic language that developed in early medieval England and has since become a English as a lingua franca, global lingua franca. The namesake of the language is the Angles (tribe), Angles, one of the Germanic peoples that Anglo-Saxon settlement of Britain, migrated to Britain after its End of Roman rule in Britain, Roman occupiers left. English is the list of languages by total number of speakers, most spoken language in the world, primarily due to the global influences of the former British Empire (succeeded by the Commonwealth of Nations) and the United States. English is the list of languages by number of native speakers, third-most spoken native language, after Mandarin Chinese and Spanish language, Spanish; it is also the most widely learned second language in the world, with more second-language speakers than native speakers. English is either the official language or one of the official languages in list of countries and territories where English ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superior Highly Composite Number
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power. For any possible exponent, whichever integer has the greatest ratio is a superior highly composite number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. The first ten superior highly composite numbers and their factorization are listed. For a superior highly composite number there exists a positive real number such that for all natural numbers we have \frac\geq\frac where , the divisor function, denotes the number of divisors of . The term was coined by Ramanujan (1915). For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composite ... [...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] |
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] |
Leonardo Prime
The Leonardo numbers are a sequence of numbers given by the recurrence: : L(n) = \begin 1 & \mbox n = 0 \\ 1 & \mbox n = 1 \\ L(n - 1) + L(n - 2) + 1 & \mbox n > 1 \\ \end Edsger W. Dijkstra used them as an integral part of his smoothsort algorithm, and also analyzed them in some detail. A Leonardo prime is a Leonardo number that is also prime. Values The first few Leonardo numbers are :1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, ... The first few Leonardo primes are : 3, 5, 41, 67, 109, 1973, 5167, 2692537, 11405773, 126491971, 331160281, 535828591, 279167724889, 145446920496281, 28944668049352441, 5760134388741632239, 63880869269980199809, 167242286979696845953, 597222253637954133837103, ... Modulo cycles The Leonardo numbers form a cycle in any modulo n≥2. An easy way to see it is: * If a pair of numbers modulo n appears twice in the sequence, then there's a cy ... [...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] |
