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Seventeen Or Bust
Seventeen or Bust was a volunteer computing project started in March 2002 to solve the last seventeen cases in the Sierpinski problem. The project solved eleven cases before a server loss in April 2016 forced it to cease operations. Work on the Sierpinski problem moved to PrimeGrid, which solved a twelfth case in October 2016. Five cases remain unsolved . Goals The goal of the project was to prove that 78557 is the smallest Sierpinski number, that is, the least odd ''k'' such that ''k''·2''n''+1 is composite (i.e. not prime) for all ''n'' > 0. When the project began, there were only seventeen values of ''k'' 0 (or else ''k'' has algebraic factorizations for some ''n'' values and a finite prime set that works only for the remaining ''n''). For example, for the smallest known Sierpinski number, 78557, the covering set is . For another known Sierpinski number, 271129, the covering set is . Each of the remaining sequences has been tested and none has a small cove ... [...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] |
Lucas–Lehmer–Riesel Test
In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form ''N'' = ''k'' ⋅ 2''n'' − 1 (Riesel numbers) with odd ''k'' < 2''n''. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form. For numbers of the form ''N'' = ''k'' ⋅ 2''n'' + 1 (Proth numbers), either application of Proth's theorem (a Las Vegas algorithm) or one of the deterministic proofs described in Brillhart-Lehmer-Selfridge 1975 (see Pocklington primality test) are used. The algorithm The algorithm is very similar to the Lucas–Lehmer test, but with a variable starting point depending on the value of ''k''. Define a sequence ''u''''i'' for all ''i'' > 0 by: : u_i = u_^2-2. \, Then ''N'' = ''k'' ⋅ 2''n'' − 1, with ''k'' < 2''n'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. *Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive number th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed Prime Searches
Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a variable **Cumulative distribution function, in which the probability of being no greater than a particular value is a function of that value *Frequency distribution, a list of the values recorded in a sample *Inner distribution, and outer distribution, in coding theory *Distribution (differential geometry), a subset of the tangent bundle of a manifold *Distributed parameter system, systems that have an infinite-dimensional state-space *Distribution of terms, a situation in which all members of a category are accounted for *Distributivity, a property of binary operations that generalises the distributive law from elementary algebra *Distribution (number theory) *Distribution problems, a common type of problems in combinatorics where the goal is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer-assisted Proof
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program. Attempts have also been made in the area of artificial intelligence research to create smaller, explicit, new proofs of mathematical theorems from the bottom up using automated reasoning techniques such as heuristic search. Such automated theorem provers have proved a number of new results and found new proofs for known theorems. Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which are nonetheless formally verified for correctness. Since these proofs ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Volunteer Computing Projects
This is a comprehensive list of volunteer computing projects; a type of distributed computing where volunteers donate computing time to specific causes. The donated computing power comes from idle CPUs and GPUs in personal computers, video game consoles and Android devices. Each project seeks to utilize the computing power of many internet connected devices to solve problems and perform tedious, repetitive research in a very cost effective manner. Active projects Completed projects See also * List of grid computing projects * List of citizen science projects * List of crowdsourcing projects * List of free and open-source Android applications This is a list of notable applications (''apps'') that run on the Android platform which meet guidelines for free software and open-source software. Advertisement blocking Web browsers Office Suites and synchronisation Co ... * List of Berkeley Open Infrastructure for Network Computing (BOINC) projects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riesel Sieve
Riesel Sieve was a volunteer computing project, running in part on the BOINC platform. Its aim was to prove that 509,203 is the smallest Riesel number, by finding a prime of the form for all odd smaller than 509,203. Progress At the start of the project in August 2003, there were less than 509,203 for which no prime was known. , 52 of these had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 502,573 × 27,181,987 − 1 of 2,162,000 digits, and it is known that for none of the remaining there is a prime with ''n'' <= 10,000,000 (As of February 2020). The project proceeds in the same way as other prime-hunting projects like or : sieving eliminates pairs (''k'', ''n'') wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novel
A novel is a relatively long work of narrative fiction, typically written in prose and published as a book. The present English word for a long work of prose fiction derives from the for "new", "news", or "short story of something new", itself from the la, novella, a singular noun use of the neuter plural of ''novellus'', diminutive of ''novus'', meaning "new". Some novelists, including Nathaniel Hawthorne, Herman Melville, Ann Radcliffe, John Cowper Powys, preferred the term "romance" to describe their novels. According to Margaret Doody, the novel has "a continuous and comprehensive history of about two thousand years", with its origins in the Ancient Greek and Roman novel, in Chivalric romance, and in the tradition of the Italian renaissance novella.Margaret Anne Doody''The True Story of the Novel'' New Brunswick, NJ: Rutgers University Press, 1996, rept. 1997, p. 1. Retrieved 25 April 2014. The ancient romance form was revived by Romanticism, especially the histori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Colbert
Stephen Tyrone Colbert ( ; born May 13, 1964) is an American comedian, writer, producer, political commentator, actor, and television host. He is best known for hosting the satirical Comedy Central program ''The Colbert Report'' from 2005 to 2014 and the CBS talk program ''The Late Show with Stephen Colbert'' beginning in September 2015. Colbert originally studied to be a dramatic actor, but became interested in improvisational theater while attending Northwestern University, where he met Second City director Del Close. Colbert first performed professionally as an understudy for Steve Carell at Second City Chicago, where his troupemates included Paul Dinello and Amy Sedaris, comedians with whom he developed the sketch comedy series ''Exit 57''. He wrote and performed on ''The Dana Carvey Show'' before collaborating with Sedaris and Dinello again on the television series ''Strangers with Candy''. He gained attention for his role on the latter as closeted gay history teacher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Pages
The PrimePages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin. The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms. , the 5,000th prime has around 412,000 digits.. Retrieved on 2018-02-12. The PrimePages has articles on primes and primality testing. It includes "The Prime Glossary" with articles on hundreds of glosses related to primes, and "Prime Curios!" with thousands of curios about specific numbers. The database started as a list of titanic primes (primes with at least 1000 decimal digits) by Samuel Yates. In subsequent years, the whole top-5,000 has consisted of gigantic primes (primes with at least 10,000 decimal digits). Primes of special forms are kept on the current lists if they are titanic and in the top-20 or top-5 for their form. See also *List of prime numbers This is a list of articles about pri ... [...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] |
