185 relations: AKS primality test, Allan J. C. Cunningham, André Gérardin, Édouard Lucas, Bernoulli number, BESK, Binomial number, Bryant Tuckerman, Carol number, Centered nonagonal number, Circular prime, CN-group, Cornwall Colts, Cunningham number, Cunningham project, Curtis Cooper (mathematician), Data compaction, David Slowinski, Derrick Henry Lehmer, Donald B. Gillies, Double Mersenne number, Duodecimal, Eisenstein prime, Elementary cellular automaton, Elliptic curve primality, Elliptic-curve cryptography, Entropia, Inc., Erdős–Borwein constant, Euclid, Euclid–Euler theorem, Experimental mathematics, Fürer's algorithm, Fermat number, Fermat pseudoprime, FLOPS, Frank Nelson Cole, Friendly number, Generating primes, George Woltman, Gigantic prime, Gillies' conjecture, Great Internet Mersenne Prime Search, Hans Riesel, Happy number, Harry L. Nelson, Hexagonal number, History of computing hardware, Holographic algorithm, IBM 7090, ILLIAC, ..., ILLIAC II, Indian Institute of Technology Roorkee, Integer sequence prime, Ivan Pervushin, Jacobi symbol, Jens Franke, June 1949, Kynea number, Lagrange's theorem (group theory), Landon Curt Noll, Large numbers, Largest known prime number, Lehmer random number generator, Leonhard Euler, Liber Abaci, Linear congruential generator, List of distributed computing projects, List of Hockey Heritage North Honoured Members, List of logarithmic identities, List of long mathematical proofs, List of number theory topics, List of numbers, List of OEIS sequences, List of perfect numbers, List of prime numbers, List of things named after Leonhard Euler, List of unsolved problems in mathematics, Lucas sequence, Lucas test, Lucas–Lehmer primality test, Lucas–Lehmer–Riesel test, M36, M40, M41, M42, M43, M44, M45, M46, M47, M48, M49, Manchester Mark 1, Marin Mersenne, Megaprime, Mersenne conjectures, Mersenne Twister, Multiplication algorithm, On-Line Encyclopedia of Integer Sequences, Orders of magnitude (numbers), Palindromic number, Palindromic prime, Pandigital number, Paul Gage, Paul T. Bateman, Perfect number, Permutable prime, Pernicious number, Peter Barlow (mathematician), Pierpont prime, Polite number, Power of two, Prime number, Prime95, Primecoin, Primitive polynomial (field theory), Proth number, Proth's theorem, Quasi-opportunistic supercomputing, Ralph Ernest Powers, Ramanujan–Nagell equation, Raphael M. Robinson, Repdigit, Repunit, Richard P. Brent, Safe prime, Scholz conjecture, Scott Kurowski, Self number, Semiperfect number, Seventeen or Bust, Solinas prime, Sophie Germain prime, Special number field sieve, Strobogrammatic number, Supercomputer, Superperfect number, SWAC (computer), The Housekeeper and the Professor, The Intimate P. D. Q. Bach, Timeline of computational mathematics, Titanic prime, Triangular number, Trygve Nagell, Unique prime, Universal hashing, University of Central Missouri, Wheat and chessboard problem, Wieferich prime, Wilhelm Ljunggren, Woodall number, 1,000,000,000, 10,000,000, 100,000, 107 (number), 11 (number), 127 (number), 1588 in science, 17 (number), 1772 in science, 1876 in science, 19 (number), 1903 in science, 1925–26 Toronto St. Patricks season, 2, 2,147,483,647, 2000 (number), 2005 in the United States, 2006 in science, 255 (number), 28 (number), 3, 31 (number), 4000 (number), 496 (number), 5, 500 (number), 6, 61 (number), 63 (number), 64 (number), 7, 8000 (number), 8128 (number), 89 (number). Expand index (135 more) » « Shrink index
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in a paper titled "PRIMES is in P".
Allan Joseph Champneys Cunningham (1842 – 1928) was a British mathematician.
André Gérardin (1879, Nancy, Meurthe-et-Moselle – 1953, Nancy, Meurthe-et-Moselle) was a French mathematician, specializing in number theory and calculating machines used in factoring large positive integers, finding primes, and calculating quadratic residues modulo a given positive integer.
François Édouard Anatole Lucas (4 April 1842 – 3 October 1891) was a French mathematician.
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
BESK (Binär Elektronisk SekvensKalkylator, Swedish for "Binary Electronic Sequence Calculator") was Sweden's first electronic computer, using vacuum tubes instead of relays.
In mathematics, specifically in number theory, a binomial number is an integer which can be obtained by evaluating a homogeneous polynomial containing two terms.
Louis Bryant Tuckerman, III (November 28, 1915 – May 19, 2002) was an American mathematician, born in Lincoln, Nebraska.
A Carol number is an integer of the form 4^n - 2^ - 1.
A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers.
A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime.
In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of: are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable.
The Cornwall Colts are a Canadian junior ice hockey team from Cornwall, Ontario, Canada.
In mathematics, specifically in number theory, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham.
The Cunningham project is a project, started in 1925, to factor numbers of the form bn ± 1 for b.
Curtis Niles Cooper is an American mathematician.
In telecommunication, data compaction is the reduction of the number of data elements, bandwidth, cost, and time for the generation, transmission, and storage of data without loss of information by eliminating unnecessary redundancy, removing irrelevancy, or using special coding.
David Slowinski is a mathematician involved in prime numbers.
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991) was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes.
Donald Bruce Gillies (October 15, 1928 – July 17, 1975) was a Canadian mathematician and computer scientist, known for his work in game theory, computer design, and minicomputer programming environments.
In mathematics, a double Mersenne number is a Mersenne number of the form where p is a prime exponent.
The duodecimal system (also known as base 12 or dozenal) is a positional notation numeral system using twelve as its base.
In mathematics, an Eisenstein prime is an Eisenstein integer that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units, itself and its associates.
In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors.
In mathematics elliptic curve primality testing techniques are among the quickest and most widely used methods in primality proving.
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
Entropia, Inc. was a company founded in 1997 that sold distributed computing software for CPU scavenging.
The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers.
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
The Euclid–Euler theorem is a theorem in mathematics that relates perfect numbers to Mersenne primes.
Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns.
Fürer's algorithm is an integer multiplication algorithm for extremely large integers with very low asymptotic complexity.
In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.
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.
Frank Nelson Cole (September 20, 1861 – May 26, 1926) was an American mathematician, born in Ashland, Massachusetts, and educated at Harvard, where he lectured on mathematics from 1885 to 1887.
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself.
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently.
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 and MPrime.
A gigantic prime is a prime number with at least 10,000 decimal digits.
In number theory, Gillies' conjecture is a conjecture about the distribution of prime divisors of Mersenne numbers and was made by Donald B. Gillies in a 1964 paper in which he also announced the discovery of three new Mersenne primes.
The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
Hans Ivar Riesel (May 28, 1929 in Stockholm – December 21, 2014) was a Swedish mathematician who discovered the 18th known Mersenne prime in 1957, using the computer BESK: this prime is 23217-1 and consists of 969 digits.
A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1.
Harry Lewis Nelson (born January 8, 1932) is an American mathematician and computer programmer.
A hexagonal number is a figurate number.
The history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers.
In computer science, a holographic algorithm is an algorithm that uses a holographic reduction.
The IBM 7090 is a second-generation transistorized version of the earlier IBM 709 vacuum tube mainframe computers that was designed for "large-scale scientific and technological applications".
ILLIAC (Illinois Automatic Computer) was a series of supercomputers built at a variety of locations, some at the University of Illinois at Urbana-Champaign.
The ILLIAC II was a revolutionary super-computer built by the University of Illinois that became operational in 1962.
Indian Institute of Technology Roorkee (abbreviated IIT Roorkee or IITR), formerly University of Roorkee and Thomason College of Civil Engineering, is a public engineering university located in Roorkee, Uttarakhand, India.
In mathematics, an integer sequence prime is a prime number found as a member of an integer sequence.
Ivan Mikheevich Pervushin (Иван Михеевич Первушин, sometimes transliterated as Pervusin or Pervouchine) (—) was a Russian clergyman and mathematician of the second half of the 19th century, known for his achievements in number theory.
Jacobi symbol for various k (along top) and n (along left side).
Jens Franke (born June 29, 1964) is a German mathematician.
The following events occurred in June 1949.
A Kynea number is an integer of the form An equivalent formula is This indicates that a Kynea number is the nth power of 4 plus the (n + 1)th Mersenne number.
Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. The theorem is named after Joseph-Louis Lagrange.
Landon Curt Noll (born October 28, 1960) is an American computer scientist, co-discoverer of the 25th Mersenne prime and discoverer of the 26th, which he found while still enrolled at Hayward High School and concurrently at California State University, Hayward.
Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions.
The largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits.
The Lehmer random number generator (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is: where the modulus n is a prime number or a power of a prime number, the multiplier g is an element of high multiplicative order modulo n (e.g., a primitive root modulo n), and the seed X is coprime to n.
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
Liber Abaci (1202, also spelled as Liber Abbaci) is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
This is a list of distributed computing and grid computing projects.
This is a list of the Honoured Members of Hockey Heritage North.
In mathematics, there are many logarithmic identities.
This is a list of unusually long mathematical proofs.
This is a list of number theory topics, by Wikipedia page.
This is a list of articles about numbers (not about numerals).
This article provides a list of integer sequences in the On-Line Encyclopedia of Integer Sequences that have their own English Wikipedia entries.
The following is a list of the known perfect numbers, and the exponents p that can be used to generate them (using the expression 2p−1× (2p − 1)) whenever 2p − 1 is a Mersenne prime.
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Leonhard Euler (1707–1783)In mathematics and physics, there are a large number of topics named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations.
Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still remain unsolved.
In mathematics, the Lucas sequences U_n(P,Q) and V_n(P, Q) are certain constant-recursive integer sequences that satisfy the recurrence relation where P and Q are fixed integers.
Lucas test may refer to.
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers.
In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N.
M36, M-36 or M.36 may refer to.
M40 or M-40 may refer to: In transportation.
M41, M-41, or M.41 may refer to.
M42 or M-42 may refer to: In science.
M43 may refer to.
M44 or M-44 may refer to.
M45 or M-45 may refer to: In science.
M46 or M-46 may refer to.
M47 or M-47 may refer to.
M48 or M-48 may refer to.
M49, M.49 or M-49 may be.
The Manchester Mark 1 was one of the earliest stored-program computers, developed at the Victoria University of Manchester from the Manchester Baby (operational in June 1948).
Marin Mersenne, Marin Mersennus or le Père Mersenne (8 September 1588 – 1 September 1648) was a French polymath, whose works touched a wide variety of fields.
A megaprime is a prime number with at least one million decimal digits (whereas titanic prime is a prime number with at least 1,000 digits, and gigantic prime has at least 10,000 digits).
In mathematics, the Mersenne conjectures concern the characterization of prime numbers of a form called Mersenne primes, meaning prime numbers that are a power of two minus one.
The Mersenne Twister is a pseudorandom number generator (PRNG).
A multiplication algorithm is an algorithm (or method) to multiply two numbers.
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities.
A palindromic number or numeral palindrome is a number that remains the same when its digits are reversed.
A palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number.
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once.
Paul Gage is a research computer scientist who works at Cray Supercomputers.
Paul Trevier Bateman (June 6, 1919 – December 26, 2012) was an American number theorist, known for formulating the Bateman–Horn conjecture on the density of prime number values generated by systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes.
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).
A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number.
In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.
Peter Barlow (13 October 1776 – 1 March 1862)Lance Day and Ian McNeil, Biographical dictionary of the history of technology, Routledge, 1995, page 42.
A Pierpont prime is a prime number of the form for some nonnegative integers and.
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers.
In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Prime95 is the freeware application written by George Woltman that is used by GIMPS, a distributed computing project dedicated to finding new Mersenne prime numbers.
Primecoin (sign: Ψ; code: XPM) is a peer-to-peer open source cryptocurrency that implements a unique scientific computing proof-of-work system.
In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF(pm).
In number theory, a Proth number, named after the mathematician François Proth, is a number of the form where k is an odd positive integer and n is a positive integer such that 2^n > k. Without the latter condition, all odd integers greater than 1 would be Proth numbers.
In number theory, Proth's theorem is a primality test for Proth numbers.
Quasi-opportunistic supercomputing is a computational paradigm for supercomputing on a large number of geographically disperse computers.
Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers.
In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two.
Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician.
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal).
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit.
Richard Peirce Brent (born 20 April 1946, Melbourne) is an Australian mathematician and computer scientist.
A safe prime is a prime number of the form 2p + 1, where p is also a prime.
In mathematics, the Scholz conjecture is a conjecture on the length of certain addition chains.
Scott Kurowski is an entrepreneurial software technologist and inventor.
A self number, Colombian number or Devlali number is an integer that cannot be written as the sum of any other integer n and the individual digits of n. This property is specific to the base used to represent the integers.
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors.
Seventeen or Bust was a distributed computing project started in March 2002 to solve the last seventeen cases in the Sierpinski problem.
In mathematics, a Solinas prime, or generalized mersenne prime, is a prime number that has the form f(2^m), where f(x) is a low-degree polynomial with small integer coefficients.
In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime.
In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm.
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees.
A supercomputer is a computer with a high level of performance compared to a general-purpose computer.
In mathematics, a superperfect number is a positive integer n that satisfies where σ is the divisor summatory function.
The SWAC (Standards Western Automatic Computer) was an early electronic digital computer built in 1950 by the U.S. National Bureau of Standards (NBS) in Los Angeles, California.
(literally "The Professor's Beloved Equation") is a novel by Yoko Ogawa set in modern-day Japan.
The Intimate P. D. Q. Bach is "a live recording of The Intimate P.D.Q. Bach stage show, featuring Professor Peter Schickele and the Semi-Pro Musica Antiqua" and was released on Vanguard Records in 1974.
This is a timeline of key developments in computational mathematics.
Titanic prime is a term coined by Samuel Yates in the 1980s, denoting a prime number of at least 1000 decimal digits.
A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.
Trygve Nagell (July 13, 1895 in Oslo – January 24, 1988 in Uppsala) was a Norwegian mathematician, known for his works on the Diophantine equations within number theory.
In recreational number theory, a unique prime or unique period prime is a certain kind of prime number.
In mathematics and computing universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below).
The University of Central Missouri (UCM), formerly Central Missouri State University (CMSU), is a public state university located in Warrensburg, Missouri, United States.
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: The problem may be solved using simple addition.
In number theory, a Wieferich prime is a prime number p such that p2 divides, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides.
Wilhelm Ljunggren (7 October 1905 – 25 January 1973) was a Norwegian mathematician, specializing in number theory.
In number theory, a Woodall number (Wn) is any natural number of the form for some natural number n. The first few Woodall numbers are.
1,000,000,000 (one billion, short scale; one thousand million or milliard, yard, long scale) is the natural number following 999,999,999 and preceding 1,000,000,001.
10,000,000 (ten million) is the natural number following 9,999,999 and preceding 10,000,001.
100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001.
107 (one hundred seven) is the natural number following 106 and preceding 108.
11 (eleven) is the natural number following 10 and preceding 12.
127 (one hundred twenty-seven) is the natural number following 126 and preceding 128.
The year 1588 in science and technology, Armada year, included a number of events, some of which are listed here.
17 (seventeen) is the natural number following 16 and preceding 18.
The year 1772 in science and technology involved some significant events.
The year 1876 in science and technology involved some significant events, listed below.
19 (nineteen) is the natural number following 18 and preceding 20.
The year 1903 in science and technology involved some significant events, listed below.
The 1925–26 Toronto St.
2 (two) is a number, numeral, and glyph.
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1.
2000 (two thousand) is a natural number following 1999 and preceding 2001.
Events from the year 2005 in the United States.
The year 2006 in science and technology involved some significant events.
255 (two hundred fifty-five) is the natural number following 254 and preceding 256.
28 (twenty-eight) is the natural number following 27 and preceding 29.
3 (three) is a number, numeral, and glyph.
31 (thirty-one) is the natural number following 30 and preceding 32.
4000 (four thousand) is the natural number following 3999 and preceding 4001.
496 (four hundred ninety-six) is the natural number following 495 and preceding 497.
5 (five) is a number, numeral, and glyph.
500 (five hundred) is the natural number following 499 and preceding 501.
6 (six) is the natural number following 5 and preceding 7.
61 (sixty-one) is the natural number following 60 and preceding 62.
63 (sixty-three) is a natural number following 62 and preceding 64.
64 (sixty-four) is the natural number following 63 and preceding 65.
7 (seven) is the natural number following 6 and preceding 8.
8000 (eight thousand) is the natural number following 7999 and preceding 8001.
8128 is the integer following 8127 and preceding 8129.
89 (eighty-nine) is the natural number following 88 and preceding 90.
131071 (number), 2305843009213693951, 2305843009213693951 (number), 242643801-1, 2^42643801-1, 2^61-1, 2^n-1, 2ⁿ-1, 524287 (number), 8191 (number), E. Fauquembergue, Factorization of composite Mersenne numbers, Gordon Spence, Joel Armengaud, Josh Findley, List of Mersenne primes, Mersene prime, Mersenne Number, Mersenne Numbers, Mersenne Prime, Mersenne Prime Numbers, Mersenne Primes, Mersenne number, Mersenne numbers, Mersenne prime number, Mersenne prime numbers, Mersenne primes, Nayan Hajratwala, Pervushin's number, Roland Clarkson, Steven Boone.