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GIMPS
The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client and its Linux port MPrime. Scott Kurowski wrote the back end PrimeNet server to demonstrate volunteer computing software by Entropia, a company he founded in 1997. GIMPS is registered as Mersenne Research, Inc. with Kurowski as Executive Vice President and board director. GIMPS is said to be one of the first large scale volunteer computing projects over the Internet for research purposes. , the project has found a total of seventeen Mersenne primes, fifteen of which were the largest known prime number at their respective times of discovery. The largest known prime is 282,589,933 − 1 (or M82,589,933 for short) and was discovered on December 7, 2018, by Patrick Laroche. On December 4, 2020, the project passed a major milestone af ... [...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 va ... [...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] |
Prime95
Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system stability. Although most of its source code is available, Prime95 is not free and open-source software because its end-user license agreement states that if the software is used to find a prime qualifying for a bounty offered by the Electronic Frontier Foundation, then that bounty will be claimed and distributed by GIMPS. Finding Mersenne primes by volunteer computing Prime95 tests numbers for primality using the Fermat primality test (referred to internally as PRP, or "probable prime"). For much of its history, it used the Lucas–Lehmer primality test, but the availability of Lucas–Lehmer assignments was deprecated in April 2021 to inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Woltman
George Woltman (born November 10, 1957) is the founder of the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project researching Mersenne prime numbers using his software Prime95. He graduated from the Massachusetts Institute of Technology (MIT) with a degree in computer science. He lives in North Carolina. His mathematical libraries created for the GIMPS project are the fastest known for multiplication of large integers, and are used by other distributed computing projects as well, such as Seventeen or Bust. He also worked on a TTL version of Maze War while a student at MIT. Later he worked as a programmer for Data General. See also * Prime95 Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing proj ... References External links The Prime Pages Titan Biogr ... [...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 alway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucas–Lehmer Primality Test
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1876 and subsequently improved by Derrick Henry Lehmer in the 1930s. The test The Lucas–Lehmer test works as follows. Let ''M''''p'' = 2''p'' − 1 be the Mersenne number to test with ''p'' an odd prime. The primality of ''p'' can be efficiently checked with a simple algorithm like trial division since ''p'' is exponentially smaller than ''M''''p''. Define a sequence \ for all ''i'' ≥ 0 by : s_i= \begin 4 & \texti=0; \\ s_^2-2 & \text \end The first few terms of this sequence are 4, 14, 194, 37634, ... . Then ''M''''p'' is prime if and only if :s_ \equiv 0 \pmod. The number ''s''''p'' − 2 mod ''M''''p'' is called the Lucas–Lehmer residue of ''p''. (Some authors equivalently set ''s''1 = 4 and test ''s''''p''−1 mod ''M''''p''). In pseudocode, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FLOPS
In computing, floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance, useful in fields of scientific computations that require floating-point calculations. For such cases, it is a more accurate measure than measuring instructions per second. Floating-point arithmetic Floating-point arithmetic is needed for very large or very small real numbers, or computations that require a large dynamic range. Floating-point representation is similar to scientific notation, except everything is carried out in base two, rather than base ten. The encoding scheme stores the sign, the exponent (in base two for Cray and VAX, base two or ten for IEEE floating point formats, and base 16 for IBM Floating Point Architecture) and the significand (number after the radix point). While several similar formats are in use, the most common is ANSI/IEEE Std. 754-1985. This standard defines the format for 32-bit numbers called ''single precision'', as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volunteer Computing
Volunteer computing is a type of distributed computing in which people donate their computers' unused resources to a research-oriented project, and sometimes in exchange for credit points. The fundamental idea behind it is that a modern desktop computer is sufficiently powerful to perform billions of operations a second, but for most users only between 10-15% of its capacity is used. Typical uses like basic word processing or web browsing leave the computer mostly idle. The practice of volunteer computing, which dates back to the mid-1990s, can potentially make substantial processing power available to researchers at minimal cost. Typically, a program running on a volunteer's computer periodically contacts a research application to request jobs and report results. A middleware system usually serves as an intermediary. History The first volunteer computing project was the Great Internet Mersenne Prime Search, which was started in January 1996. It was followed in 1997 by distribute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software
Software is a set of computer programs and associated software documentation, documentation and data (computing), data. This is in contrast to Computer hardware, hardware, from which the system is built and which actually performs the work. At the low level language, lowest programming level, executable code consists of Machine code, machine language instructions supported by an individual Microprocessor, processor—typically a central processing unit (CPU) or a graphics processing unit (GPU). Machine language consists of groups of Binary number, binary values signifying Instruction set architecture, processor instructions that change the state of the computer from its preceding state. For example, an instruction may change the value stored in a particular storage location in the computer—an effect that is not directly observable to the user. An instruction System call, may also invoke one of many Input/output, input or output operations, for example displaying some text on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hewlett-Packard
The Hewlett-Packard Company, commonly shortened to Hewlett-Packard ( ) or HP, was an American multinational information technology company headquartered in Palo Alto, California. HP developed and provided a wide variety of hardware components, as well as software and related services to consumers, small and medium-sized businesses ( SMBs), and large enterprises, including customers in the government, health, and education sectors. The company was founded in a one-car garage in Palo Alto by Bill Hewlett and David Packard in 1939, and initially produced a line of electronic test and measurement equipment. The HP Garage at 367 Addison Avenue is now designated an official California Historical Landmark, and is marked with a plaque calling it the "Birthplace of 'Silicon Valley'". The company won its first big contract in 1938 to provide test and measurement instruments for Walt Disney's production of the animated film ''Fantasia'', which allowed Hewlett and Packard to formally es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Machine
In computing, a virtual machine (VM) is the virtualization/ emulation of a computer system. Virtual machines are based on computer architectures and provide functionality of a physical computer. Their implementations may involve specialized hardware, software, or a combination. Virtual machines differ and are organized by their function, shown here: * '' System virtual machines'' (also termed full virtualization VMs) provide a substitute for a real machine. They provide functionality needed to execute entire operating systems. A hypervisor uses native execution to share and manage hardware, allowing for multiple environments which are isolated from one another, yet exist on the same physical machine. Modern hypervisors use hardware-assisted virtualization, virtualization-specific hardware, primarily from the host CPUs. * Process virtual machines are designed to execute computer programs in a platform-independent environment. Some virtual machine emulators, such as QEMU a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TOP500
The TOP500 project ranks and details the 500 most powerful non- distributed computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year. The first of these updates always coincides with the International Supercomputing Conference in June, and the second is presented at the ACM/IEEE Supercomputing Conference in November. The project aims to provide a reliable basis for tracking and detecting trends in high-performance computing and bases rankings on HPL, a portable implementation of the high-performance LINPACK benchmark written in Fortran for distributed-memory computers. The 60th TOP500 was published in November 2022. Since June 2022, USA's Frontier is the most powerful supercomputer on TOP500, reaching 1102 petaFlops (1.102 exaFlops) on the LINPACK benchmarks. The United States has by far the highest share of total computing power on the list (nearly 50%), while China currently leads the list in number of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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