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PrimePages
The PrimePages is a website about prime numbers originally created by Chris Caldwell at the University of Tennessee at Martin who maintained it from 1994 to 2023. 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 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 1984. On March 11, 2023, the PrimePages moved from primes.utm.edu to t5k.org, and is no longer maintained by Caldwell. See also * List of largest known primes and probable primes *List of prime numbers This is a list of articles about prime numbers. A prime number (or ''prime'') is a natural number greater than 1 that has no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Largest Known Primes And Probable Primes
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown. Largest known primes These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers. “!” is the factorial, “#” is the primorial, and \Phi_3(x) is the third cyclotomic polynomial, defined as x^2 + x + 1. Largest known probable primes (PRPs) These are probable primes. Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes. F(''n'') is the ''n''th Fibonacci number. , data-sort-value"1 December 2023" , December 2023 , 2,239,990 , - , _row_count , \tfrac , 1 March 2018 , 2,201,714 , - , _row_count , \tfrac , data-sort-value"1 December 2023" , December 2023 , 2,181,134 , - , _row_count , \tf ... [...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 (mathematics), 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 factorization, 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 primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Tennessee At Martin
The University of Tennessee at Martin (UT Martin or UTM) is a public university in Martin, Tennessee, United States. It is one of the five campuses of the University of Tennessee system. UTM is the only public university in West Tennessee outside of Memphis. UTM operates a large experimental farm and several satellite centers in West Tennessee. History Although UT Martin dates from 1927, it is not the first educational institution to use the current site. In 1900, Ada Gardner Brooks donated a site on what was then the outskirts of Martin to the Tennessee Baptist Convention for the purposes of opening a school. The school opened as the Hall-Moody Institute, named for two local Baptist ministers – John Newton Hall and Joseph Burnley Moody. It originally offered 13 years of study, from elementary grades to the equivalent of the first years of collegiate work. The institute changed its name to Hall-Moody Normal School in 1917, as teacher training became its primary focus. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primality Test
A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is prime, while others like Miller–Rabin prove that a number is composite. Therefore, the latter might more accurately be called ''compositeness tests'' instead of primality tests. Simple methods The simplest primality test is '' trial division'': given an input number, n, check whether it is divisible by any prime number between 2 and \sqrt n (i.e., whether the division leaves no remainder). If so, then n is composite. Otherwise, it is prime.Riesel (1994) pp.2-3 For any divisor p \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel Yates
Samuel Yates (May 10, 1919 in Savannah, Georgia – April 22, 1991 in New Brunswick, New Jersey) was a computer engineer and mathematician who first described unique primes in 1980. In 1984 he began the list of "Largest Known Primes" (today The Prime Pages) and coined the name titanic prime for any prime with 1,000 or more decimal digits. He also called those who proved their primality "titans". He also coined the term gigantic prime for any prime with 10,000 or more decimal digits. He is the author of ''Repunits and Repetends''. Education and Career Between 1940 and 1973 Yates worked a number of different positions at the United States Army Corps of Engineers, Aero Service Corporation, United States Army Map Service and Radio Corporation of America before becoming a mathematical researcher from 1973. He attained a Bachelor in Mathematics from George Washington University, a Master of Science in Electrical Engineering from the University of Pennsylvania The U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Prime Numbers
This is a list of articles about prime numbers. A prime number (or ''prime'') is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. 1 is neither prime nor composite. The first 1000 prime numbers The following table lists the first 1000 primes, with 20 columns of consecutive primes in each of the 50 rows. . The Goldbach conjecture verification project reports that it has computed all primes smaller than 4×10. That means 95,676,260,903,887,607 primes (nearly 10), but they were not stored. There are known formulae to evaluate the prime-counting function (the number of primes smaller than a given value) faster than computing the primes. This has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Numbers
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 , called trial division, tests whether is a multiple of any integer between 2 and . 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 produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Websites
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Educational Websites
American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, people who self-identify their ancestry as "American" ** American English, the set of varieties of the English language native to the United States ** Native Americans in the United States, indigenous peoples of the United States * American, something of, from, or related to the Americas, also known as "America" ** Indigenous peoples of the Americas * American (word), for analysis and history of the meanings in various contexts Organizations * American Airlines, U.S.-based airline headquartered in Fort Worth, Texas * American Athletic Conference, an American college athletic conference * American Recordings (record label), a record label that was previously known as Def American * American University, in Washington, D.C. Sports teams S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Databases In The United States
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data have become widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash cards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
