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MPrime
Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application software, 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-available software, 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 assig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pollard's P − 1 Algorithm
Pollard's ''p'' − 1 algorithm is a number theory, number theoretic integer factorization algorithm, invented by John Pollard (mathematician), John Pollard in 1974. It is a special-purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm. The factors it finds are ones for which the number preceding the factor, ''p'' − 1, is smooth number#Powersmooth numbers, powersmooth; the essential observation is that, by working in the multiplicative group Modular arithmetic, modulo a composite number ''N'', we are also working in the multiplicative groups modulo all of ''Ns factors. The existence of this algorithm leads to the concept of safe primes, being primes for which ''p'' − 1 is two times a Sophie Germain prime ''q'' and thus minimally smooth. These primes are sometimes construed as "safe for cryptographic purposes", but they m ... [...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 should 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–Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great Internet Mersenne Prime Search
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 (computing), 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 eighteen Mersenne primes, sixteen of which were the largest known prime number at their respective times of discovery. The largest known prime number, prime is 2136,279,841 − 1 (or M136,279,841 for short) and was discovered on October 12, 2024, by Luke Durant. On December 4, 2020, the project ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Windows 7
Windows 7 is a major release of the Windows NT operating system developed by Microsoft. It was Software release life cycle#Release to manufacturing (RTM), released to manufacturing on July 22, 2009, and became generally available on October 22, 2009. It is the successor to Windows Vista, released nearly three years earlier. Windows 7's Windows Server, server counterpart, Windows Server 2008 R2, was released at the same time. It sold over 630 million copies before it was succeeded by Windows 8 in October 2012. Extended support ended on January 14, 2020, over 10 years after the release of Windows 7, and the operating system ceased receiving further updates. A paid support program was available for enterprises, providing security updates for Windows 7 for up to three years since the official end of life. Windows 7 was intended to be an incremental upgrade to Windows Vista, addressing the previous OS's poor reception while maintaining hardware and software compatibility as well as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Frontier Foundation
The Electronic Frontier Foundation (EFF) is an American international non-profit digital rights group based in San Francisco, California. It was founded in 1990 to promote Internet civil liberties. It provides funds for legal defense in court, presents ''amicus curiae'' briefs, defends individuals and new Technology, technologies from what it considers abusive legal threats, works to expose government malfeasance, provides guidance to the government and courts, organizes political action and mass mailings, supports some new technologies which it believes preserve Liberty, personal freedoms and online civil liberties, maintains a database and web sites of related news and information, monitors and challenges potential legislation that it believes would infringe on Liberty, personal liberties and fair use, and solicits a list of what it considers are Patent misuse, abusive patents with intentions to defeat those that it considers are without merit (law), merit. History Foundat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug tracking system, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, GitHub, Inc. has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. GitHub reported having over 100 million developers and more than 420 million Repository (version control), repositories, including at least 28 million public repositories. It is the world's largest source code host Over five billion developer contributions were made to more than 500 million open source projects in 2024. About Founding The development of the GitHub platform began on October 19, 2005. The site was launched in April 2008 by Tom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Processing Unit
A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs). The form, CPU design, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic operation, arithmetic and Bitwise operation, logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the #Fetch, fetching (from memory), #Decode, decoding and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nvidia
Nvidia Corporation ( ) is an American multinational corporation and technology company headquartered in Santa Clara, California, and incorporated in Delaware. Founded in 1993 by Jensen Huang (president and CEO), Chris Malachowsky, and Curtis Priem, it designs and supplies graphics processing units (GPUs), application programming interfaces (APIs) for data science and high-performance computing, and system on a chip units (SoCs) for mobile computing and the automotive market. Nvidia is also a leading supplier of artificial intelligence (AI) hardware and software. Nvidia outsources the manufacturing of the hardware it designs. Nvidia's professional line of GPUs are used for edge-to-cloud computing and in supercomputers and workstations for applications in fields such as architecture, engineering and construction, media and entertainment, automotive, scientific research, and manufacturing design. Its GeForce line of GPUs are aimed at the consumer market and are used in ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Williams's P + 1 Algorithm
In computational number theory, Williams's ''p'' + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982. It works well if the number ''N'' to be factored contains one or more prime factors ''p'' such that ''p'' + 1 is smooth, i.e. ''p'' + 1 contains only small factors. It uses Lucas sequences to perform exponentiation in a quadratic field. It is analogous to Pollard's ''p'' − 1 algorithm. Algorithm Choose some integer ''A'' greater than 2 which characterizes the Lucas sequence: :V_0=2, V_1=A, V_j=AV_-V_ where all operations are performed modulo ''N''. Then any odd prime ''p'' divides \gcd(N,V_M-2) whenever ''M'' is a multiple of p-(D/p), where D=A^2-4 and (D/p) is the Jacobi symbol. We require that (D/p)=-1, that is, ''D'' should be a quadratic non-residue modulo ''p''. But as we don't know ''p'' beforehand, more than one value of ''A'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lenstra Elliptic-curve Factorization
The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose factoring, ECM is the third-fastest known factoring method. The second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra. Practically speaking, ECM is considered a special-purpose factoring algorithm, as it is most suitable for finding small factors. , it is still the best algorithm for divisors not exceeding 50 to 60 digits, as its running time is dominated by the size of the smallest factor ''p'' rather than by the size of the number ''n'' to be factored. Frequently, ECM is used to remove small factors from a very large integer with many factors; if the remaining integer is still composite, then it has only large factors and is factored ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphics Processing Unit
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs were later found to be useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. History 1970s Arcade system boards have used specialized graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trial Division
Trial division is the most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer , the integer to be factored, can be divided by each number in turn that is less than or equal to the square root of . For example, to find the prime factors of , one can try to divide by successive primes: first, ; next, neither nor evenly divides ; finally, , and is itself prime. So . Trial division was first described by Fibonacci in his book '' Liber Abaci'' (1202). Method Given an integer ''n'' (''n'' refers to "the integer to be factored"), the trial division consists of systematically testing whether ''n'' is divisible by any smaller number. Clearly, it is only worthwhile to test candidate factors less than ''n'', and in order from two upwards because an arbitrary ''n'' is more likely to be divisible by two than by three, and so on. With this ordering, there is no point in testing for divisibili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
