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2,147,483,647
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 t ... [...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] |
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 19 January 2038. The problem exists in systems which measure Unix time – the number of seconds elapsed since the ''Unix epoch'' (00:00:00 UTC on 1 January 1970) – and store it in a signed 32-bit integer. The data type is only capable of representing integers between −(2) and 231 − 1, meaning the latest time that can be properly encoded is 2 − 1 seconds after epoch (03:14:07 UTC on 19 January 2038). Attempting to increment to the following second (03:14:08) will cause the integer to overflow, setting its value to −(2) which systems will interpret as 2 seconds ''before'' epoch (20:45:52 UTC on 13 December 1901). The problem is similar in nature to the year 2000 problem. Computer systems that use time for critical computations may encounter fatal errors if the Y2038 pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Known Prime
The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilise a specialised primality test that is faster than the general one. , the eight largest known primes are Mersenne primes. The last seventeen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all 1's, since the binary form of 2''k'' − 1 is simply ''k'' 1's. Current record The record is currently held by with 24,862,048 digits, found by GIMPS in December 2018. The first and last 120 digits of its val ... [...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] |
Largest Known Prime Number
The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilise a specialised primality test that is faster than the general one. , the eight largest known primes are Mersenne primes. The last seventeen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all 1's, since the binary form of 2''k'' − 1 is simply ''k'' 1's. Current record The record is currently held by with 24,862,048 digits, found by GIMPS in December 2018. The first and last 120 digits of its val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
32-bit
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in 32-bit units. Compared to smaller bit widths, 32-bit computers can perform large calculations more efficiently and process more data per clock cycle. Typical 32-bit personal computers also have a 32-bit address bus, permitting up to 4 GB of RAM to be accessed; far more than previous generations of system architecture allowed. 32-bit designs have been used since the earliest days of electronic computing, in experimental systems and then in large mainframe and minicomputer systems. The first hybrid 16/32-bit microprocessor, the Motorola 68000, was introduced in the late 1970s and used in systems such as the original Apple Macintosh. Fully 32-bit microprocessors such as the Motorola 68020 and Intel 80386 were launched in the early to mid 1980s and became dominant by the early 1990s. This generation of personal computers coincided ... [...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] |
Arithmetic Overflow
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the ch ... [...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] |
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] |
