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911 (number)
911 (nine hundred [and] eleven) is the integer following 910 and preceding 912. It is a prime number, a Sophie Germain prime and the sum of three consecutive primes (293 + 307 + 311). It is an Eisenstein prime with no imaginary part and real part of the form 3''n'' − 1. Since 913 is a semiprime, 911 is a Chen prime. It is also a centered decagonal number. There are 911 inverse semigroups of order 7 911 is obtained by Concatenation, concatenating its product of digits and sum of digits. See also * 9-1-1, a North American emergency telephone number * 9/11, the September 11 attacks of 2001 * AD 911, a year * Porsche 911, a sports car References [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
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 alw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophie Germain Prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat’s Last Theorem was to let ''p'' be a prime number of the form 8''k'' + 7 and to let ''n'' = ''p'' – 1. In this case, x^n + y^n = z^n is unsolvable. Germain’s proof, however, remained unfinished. Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theorem which states that if ''p'' is an odd prime and 2''p'' + 1 is also prime, then ''p'' must divide ''x'', ''y'', or ''z.'' Otherwise, x^n + y^n \neq z^n. This case where ''p'' does not divide ''x'', ''y'', or ''z'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eisenstein Prime
In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself and its associates. The associates (unit multiples) and the complex conjugate of any Eisenstein prime are also prime. Characterization An Eisenstein integer is an Eisenstein prime if and only if either of the following (mutually exclusive) conditions hold: # is equal to the product of a unit and a natural prime of the form (necessarily congruent to ), # is a natural prime (necessarily congruent to 0 or ). It follows that the square of the absolute value of every Eisenstein prime is a natural prime or the square of a natural prime. In base 12 (written with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , ): The natural Eisenstein primes are exactly the natural primes ending with 5 or (i.e. the natural primes congruent to ). (The natural prime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes. Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: Formula for number of semiprimes A semiprime counting formula was discovered by E. Noel and G. Panos in 2005. Let \pi_2(n) denote the number of semiprimes less than or equal to n. Then \pi_2(n) = \sum_^ pi(n/p_k) - k + 1 /math> w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Prime
A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime. The first few Chen primes are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, … . The first few Chen primes that are not the lower member of a pair of twin primes are :2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, ... . The first few non-Chen primes are :43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, … . All of the supersingular primes are Chen primes. Rudolf Ondrejka discovered the following 3 × 3 magic square of nin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Decagonal Number
A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for ''n'' is given by the formula :5n^2+5n+1 \, Thus, the first few centered decagonal numbers are : 1, 11, 31, 61, 101 101 may refer to: * 101 (number), the number * AD 101, a year in the 2nd century AD * 101 BC, a year in the 2nd century BC It may also refer to: Entertainment * ''101'' (album), a live album and documentary by Depeche Mode * "101" (song), a ..., 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, ... Like any other centered ''k''-gonal number, the ''n''th centered decagonal number can be reckoned by multiplying the (''n'' − 1)th triangular number by ''k'', 10 in this case, then adding 1. As a consequence of performing the calculation in base 10, the centered decagonal numbers can be obtained by simply adding a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Semigroup
In group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy'', i.e. a regular semigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries. (The convention followed in this article will be that of writing a function on the right of its argument, e.g. ''x f'' rather than ''f(x)'', and composing functions from left to right—a convention often observed in semigroup theory.) Origins Inverse semigroups were introduced independently by Viktor Vladimirovich Wagner in the Soviet Union in 1952, and by Gordon Preston in the United Kingdom in 1954. Both authors arrived at inverse semigroups via the study of partial bijections of a set: a partial transformation ''α'' of a set ''X'' is a function from ''A'' to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator. The + (plus) operator is often overloaded to denote concatenation for string arguments: "Hello, " + "World" has the value "Hello, World". In other languages there is a separate operator, particularly to specify implicit type conversion to string, as opposed to more complicated behavior for generic plus. Examples include . in Edinburgh IMP, Perl, and PHP, .. in Lua, and & in Ada, AppleScript, and Visual Basic. Other syntax exists, like , , in PL/I and Oracle Database SQL. In a few languages, notably C, C++, and Python, there is string literal concatenation, m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9-1-1
, usually written 911, is an emergency telephone number for the United States, Canada, Mexico, Panama, Palau, Argentina, Philippines, Jordan, as well as the North American Numbering Plan (NANP), one of eight N11 codes. Like other emergency numbers around the world, this number is intended for use in emergency circumstances only. Using it for any other purpose (such as making false or prank calls) is a crime in most jurisdictions. In over 98% of locations in Argentina, Panama, Belize, Anguilla, Costa Rica, Ecuador, Jordan, Ethiopia, Liberia, Saudi Arabia, Philippines, Uruguay, United States, Palau, Mexico, Tonga and Canada, dialing "9-1-1" from any telephone will link the caller to an emergency dispatch office—called a Public Safety Answering Point (PSAP) by the telecommunications industry—which can send emergency responders to the caller's location in an emergency. In approximately 96 percent of the United States, the enhanced 9-1-1 system automatically pairs cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9/11
The September 11 attacks, commonly known as 9/11, were four coordinated Suicide attack, suicide List of terrorist incidents, terrorist attacks carried out by al-Qaeda against the United States on Tuesday, September 11, 2001. That morning, Hijackers in the September 11 attacks, nineteen terrorists Aircraft hijacking, hijacked four commercial Airliner, airliners scheduled to travel from the Northeastern United States to California. The hijackers crashed the first two planes into the Twin Towers of the World Trade Center (1973–2001), World Trade Center in New York City, and the third plane into the Pentagon (the headquarters of the United States Department of Defense, United States military) in Arlington County, Virginia. The fourth plane was intended to hit a Federal government of the United States, federal government building in Washington, D.C., but crashed in a field following a passenger revolt. The attacks killed nearly 3,000 people and instigated the war on terror. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AD 911
__NOTOC__ 911 (Roman numerals, CMXI) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. Events By place Europe * September 24 — King Louis the Child, Louis IV (the Child), the last ruler of the Carolingian dynasty, Carolingian Dynasty, dies at Frankfurt, Frankfurt am Main after an 11-year reign. The East Frankish dukes elect Conrad I of Germany, Conrad I at Forchheim as the king of the East Francia, East Frankish Kingdom. Charles III is elected as king of Lotharingia. Conrad is chosen through the influence of Louis' guardian and regent, Hatto I (archbishop of Mainz), Hatto I, archbishop of Mainz. * Autumn – King Charles the Simple, Charles III (the Simple) and Rollo, leader of the Vikings, sign a peace agreement (Treaty of Saint-Clair-sur-Epte). In return for his homage and conversion to Christianity, Rollo becomes a vassal and is made Duke of Normandy, Count of Rouen; this is the beginning of the duchy of Normand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Porsche 911
The Porsche 911 (pronounced ''Nine Eleven'' or in german: Neunelfer) is a two-door 2+2 high performance rear-engined sports car introduced in September 1964 by Porsche AG of Stuttgart, Germany. It has a rear-mounted flat-six engine and originally a torsion bar suspension. The car has been continuously enhanced through the years but the basic concept has remained unchanged.Corlett, p. 12 The engines were air-cooled until the introduction of the 996 series in 1998. The 911 has been raced extensively by private and factory teams, in a variety of classes. It is among the most successful competition cars. In the mid-1970s, the naturally aspirated 911 Carrera RSR won world championship races including Targa Florio and the 24 Hours of Daytona. The 911-derived 935 turbo also won the 24 Hours of Le Mans in 1979. Porsche won the World Championship for Makes in 1976, 1977, 1978, and 1979 with 911-derived models. In a 1999 poll to determine the Car of the Century, the 911 was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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