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2147483647
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on Pietro Cataldi's method, so that at most 372 divisions were needed. It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the largest known prime until 1867. In computing, this number is the largest value that a signed 32-bit integer field can hold. Barlow's prediction At the time of its discovery, 2,147,483,647 was the largest known prime number. In 1811, Peter Barlow, not anticipating future interest in perfect numbers, wrote (in ''An Elementary Investigation of the Theory of Numbers''): Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Mersenne Number
In mathematics, a double Mersenne number is a Mersenne number of the form :M_ = 2^-1 where ''p'' is prime. Examples The first four terms of the sequence of double Mersenne numbers areChris Caldwell''Mersenne Primes: History, Theorems and Lists''at the Prime Pages. : :M_ = M_3 = 7 :M_ = M_7 = 127 :M_ = M_ = 2147483647 :M_ = M_ = 170141183460469231731687303715884105727 Double Mersenne primes A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number ''M''''p'' can be prime only if ''p'' is prime, (see Mersenne prime for a proof), a double Mersenne number M_ can be prime only if ''M''''p'' is itself a Mersenne prime. For the first values of ''p'' for which ''M''''p'' is prime, M_ is known to be prime for ''p'' = 2, 3, 5, 7 while explicit factors of M_ have been found for ''p'' = 13, 17, 19, and 31. Thus, the smallest candidate for the next double Mersenne prime is M_, or 22305843009213693951 − 1. Being approximately 1.695, this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unix Epoch
Current Unix time () Unix time is a date and time representation widely used in computing. It measures time by the number of seconds that have elapsed since 00:00:00 UTC on 1 January 1970, the beginning of the Unix epoch, less adjustments made due to leap seconds. Unix time originated as the system time of Unix operating systems. It has come to be widely used in other computer operating systems, file systems, programming languages, and databases. Definition Two layers of encoding make up Unix time. The first layer encodes a point in time as a scalar real number which represents the number of seconds that have passed since 00:00:00UTC on Thursday, 1 January 1970. The second layer encodes that number as a sequence of bits or decimal digits. Unix time differs from both Coordinated Universal Time (UTC) and International Atomic Time (TAI) in its handling of leap seconds. UTC includes leap seconds that adjust for the discrepancy between precise time, as measured by atomic clock ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." Euler is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Barlow (mathematician)
Peter Barlow (13 October 1776 – 1 March 1862)Lance Day and Ian McNeil, ''Biographical dictionary of the history of technology'', Routledge, 1995, page 42. was an English mathematician and physicist. Work in mathematics In 1801, Barlow was appointed assistant mathematics master at the Royal Military Academy, Woolwich, and retained this post until 1847. He contributed articles on mathematics to ''The Ladies' Diary'' as well as publishing books such as: ''An Elementary Investigation of the Theory of Numbers''(1811); ''A New Mathematical and Philosophical Dictionary''(1814); and ''New Mathematical Tables''(1814). The latter became known as ''Barlow's Tables'' and gives squares, cubes, square roots, cube roots, and reciprocals of all integer numbers from 1 to 10,000. These tables were regularly reprinted until 1965, when computers rendered them obsolete. He contributed to ''Rees's Cyclopædia'' articles on Algebra, Analysis, Geometry and Strength of Materials. Barlow also contribu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pietro Cataldi
Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered the sixth and seventh perfect numbers by 1588.Caldwell, Chris''The largest known prime by year'' His discovery of the 6th, that corresponding to p=17 in the formula Mp=2p-1, exploded a many-times repeated number-theoretical myth that the perfect numbers had units digits that invariably alternated between 6 and 8. (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim, with a few more repeating this afterward, according to L.E.Dickson's ''History of the Theory of Numbers''). Cataldi's discovery of the 7th (for p=19) held the record for the largest known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer (computer Science)
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer. Value and representation The ''value'' of an item with an integral type is the mathematical integer that it corresponds to. Integral types may be ''unsigned'' (capable of representing only non-negative integers) or ''signed'' (capable of representing negative integers as well). An integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or −. Some programming languages allow oth ... [...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 always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metadata
Metadata is "data that provides information about other data", but not the content of the data, such as the text of a message or the image itself. There are many distinct types of metadata, including: * Descriptive metadata – the descriptive information about a resource. It is used for discovery and identification. It includes elements such as title, abstract, author, and keywords. * Structural metadata – metadata about containers of data and indicates how compound objects are put together, for example, how pages are ordered to form chapters. It describes the types, versions, relationships, and other characteristics of digital materials. * Administrative metadata – the information to help manage a resource, like resource type, permissions, and when and how it was created. * Reference metadata – the information about the contents and quality of statistical data. * Statistical metadata – also called process data, may describe processes that collect, process, or produce st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time T
The C date and time functions are a group of functions in the standard library of the C programming language implementing date and time manipulation operations. They provide support for time acquisition, conversion between date formats, and formatted output to strings. Overview of functions The C date and time operations are defined in the time.h header file (ctime header in C++). The and related types were originally proposed by Markus Kuhn to provide a variety of time bases, but only was accepted. The functionalities were, however, added to C++ in 2020 in std::chrono. Example The following C source code prints the current time to the standard output stream. #include #include #include int main(void) The output is: Current time is Thu Sep 15 21:18:23 2016 See also * Unix time * Year 2038 problem The year 2038 problem (also known as Y2038, Y2K38, or the Epochalypse) is a time formatting bug in computer systems with representing times after 03:14:07 UTC on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operations center in Piscataway, New Jersey. The mission of the IEEE is ''advancing technology for the benefit of humanity''. The IEEE was formed from the amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers in 1963. Due to its expansion of scope into so many related fields, it is simply referred to by the letters I-E-E-E (pronounced I-triple-E), except on legal business documents. , it is the world's largest association of technical professionals with more than 423,000 members in over 160 countries around the world. Its objectives are the educational and technical advancement of electrical and electronic engineering, telecommunications, computer engineering and similar disciplines. History Origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
