  Communication
Free Faster access than browser!

# Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. 

## Alan Turing

Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.

## Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

## Arjen Lenstra

Arjen Klaas Lenstra (born 2 March 1956, Groningen) is a Dutch mathematician.

## Asteroid

Asteroids are minor planets, especially those of the inner Solar System.

## Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

## Athlon

Athlon is the brand name applied to a series of x86-compatible microprocessors designed and manufactured by Advanced Micro Devices (AMD).

## Aurifeuillean factorization

In number theory, an aurifeuillean factorization, or aurifeuillian factorization, named after Léon-François-Antoine Aurifeuille, is a special type of algebraic factorization that comes from non-trivial factorizations of cyclotomic polynomials over the integers.

## Édouard Lucas

François Édouard Anatole Lucas (4 April 1842 – 3 October 1891) was a French mathematician.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## BESK

BESK (Binär Elektronisk SekvensKalkylator, Swedish for "Binary Electronic Sequence Calculator") was Sweden's first electronic computer, using vacuum tubes instead of relays.

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

## Bryant Tuckerman

Louis Bryant Tuckerman, III (November 28, 1915 – May 19, 2002) was an American mathematician, born in Lincoln, Nebraska.

## CDC Cyber

The CDC Cyber range of mainframe-class supercomputers were the primary products of Control Data Corporation (CDC) during the 1970s and 1980s.

## Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Composite number

A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.

## Congruence relation

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure.

## Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

## Cray C90

The Cray C90 series (initially named the Y-MP C90) was a vector processor supercomputer launched by Cray Research in 1991.

## Cray T90

The Cray T90 series (code-named Triton during development) was the last of a line of vector processing supercomputers manufactured by Cray Research, Inc, superseding the Cray C90 series.

## Cray X-MP

The Cray X-MP is a supercomputer designed, built and sold by Cray Research.

## Cray-1

The Cray-1 was a supercomputer designed, manufactured and marketed by Cray Research.

## Cray-2

The Cray-2 is a supercomputer with four vector processors made by Cray Research starting in 1985.

## Cullen number

In mathematics, a Cullen number is a natural number of the form n \cdot 2^n + 1 (written C_n).

## Cult following

A cult following is a group of fans who are highly dedicated to a work of culture, often referred to as a cult classic.

## Curtis Cooper (mathematician)

Curtis Niles Cooper is an American mathematician.

## Cyclotomic polynomial

In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any.

## David Slowinski

David Slowinski is a mathematician involved in prime numbers.

## Dell Dimension

The Dell Dimension series was a line of home and business desktop computers manufactured by Dell.

## Dell OptiPlex

OptiPlex is a line of desktop computers from Dell aimed at the corporate, government and education markets.

## Derrick Henry Lehmer

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.

## Distributed computing

Distributed computing is a field of computer science that studies distributed systems.

## Donald B. Gillies

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.

## Double Mersenne number

In mathematics, a double Mersenne number is a Mersenne number of the form where p is a prime exponent.

## E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

## Eisenstein integer

In mathematics, Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are complex numbers of the form where and are integers and is a primitive (hence non-real) cube root of unity.

## Electronic Frontier Foundation

The Electronic Frontier Foundation (EFF) is an international non-profit digital rights group based in San Francisco, California.

## Erdős–Borwein constant

The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers.

## Euclid

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".

## Euclid's theorem

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

## Euclid–Euler theorem

The Euclid–Euler theorem is a theorem in mathematics that relates perfect numbers to Mersenne primes.

## Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.

## Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

## Fermat number

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.

## Fermat primality test

The Fermat primality test is a probabilistic test to determine whether a number is a probable prime.

## Fermat's little theorem

Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.

## Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

## Fourth power

In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together.

## Frank Nelson Cole

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.

## French people

The French (Français) are a Latin European ethnic group and nation who are identified with the country of France.

## Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

## Gigantic prime

A gigantic prime is a prime number with at least 10,000 decimal digits.

## Gillies' conjecture

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.

## 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.

## Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## Hans Riesel

Hans Ivar Riesel (May 28, 1929 in Stockholm &ndash; 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.

## Harry L. Nelson

Harry Lewis Nelson (born January 8, 1932) is an American mathematician and computer programmer.

## Harwell, Oxfordshire

Harwell is a village and civil parish in the Vale of White Horse about west of Didcot, roughly east of Wantage and approximately south of Oxford.

## Hexagonal number

A hexagonal number is a figurate number.

## Iamblichus

Iamblichus (Ἰάμβλιχος, c. AD 245 – c. 325), was a Syrian Neoplatonist philosopher of Arab origin.

## IBM 7090

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".

## IBM Aptiva

The IBM Aptiva personal computer was introduced in September 1994 as the replacement for the IBM PS/1.

## IBM System/360

The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## ILLIAC II

The ILLIAC II was a revolutionary super-computer built by the University of Illinois that became operational in 1962.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integer (computer science)

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.

## Integer factorization records

Integer factorization is the process of determining which prime numbers divide a given positive integer.

## Intel Core

Intel Core is a line of mid-to-high end consumer, workstation, and enthusiast central processing units (CPU) marketed by Intel Corporation.

## Introduction to Arithmetic

The book Introduction to Arithmetic (Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60&ndash;120 AD).

## Ivan Pervushin

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.

## Landon Curt Noll

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.

## Largest known prime number

The largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits.

## Lehmer random number generator

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

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.

## List of Intel Core i5 microprocessors

The following is a list of Intel Core i5 brand microprocessors.

## List of Intel Core i7 microprocessors

The following is a list of Intel Core i7 brand microprocessors.

## List of minor planets: 8001–9000

#fefefe | 8193 Ciaurro || 1993 SF || September 17, 1993 || Stroncone || Santa Lucia Obs.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Lucas sequence

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–Lehmer primality test

In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers.

## Manchester Mark 1

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 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.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Megaprime

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).

## Mersenne conjectures

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.

## Mersenne Twister

The Mersenne Twister is a pseudorandom number generator (PRNG).

## Minim (religious order)

The Minims (also called the Minimi or Order of Minims, abbreviated O.M.) are members of a Roman Catholic religious order of friars founded by Saint Francis of Paola in fifteenth-century Italy.

## Minor planet

A minor planet is an astronomical object in direct orbit around the Sun (or more broadly, any star with a planetary system) that is neither a planet nor exclusively classified as a comet.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

## Multiplicative order

In number theory, given an integer a and a positive integer n with gcd(a,n).

## National Institute of Standards and Technology

The National Institute of Standards and Technology (NIST) is one of the oldest physical science laboratories in the United States.

## NEC SX architecture

The SX series are vector supercomputers designed, manufactured, and marketed by NEC.

## New Scientist

New Scientist, first published on 22 November 1956, is a weekly, English-language magazine that covers all aspects of science and technology.

## Nicomachus

Nicomachus of Gerasa (Νικόμαχος; c. 60 &ndash; c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.

## Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

## On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

## Paul Gage

Paul Gage is a research computer scientist who works at Cray Supercomputers.

## Pentium

Pentium is a brand used for a series of x86 architecture-compatible microprocessors produced by Intel since 1993.

## Pentium 4

Pentium 4 is a brand by Intel for an entire series of single-core CPUs for desktops, laptops and entry-level servers.

## Pentium II

The Pentium II brand refers to Intel's sixth-generation microarchitecture ("P6") and x86-compatible microprocessors introduced on May 7, 1997.

## Perfect number

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).

## Perfect power

In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer.

## Pernicious number

In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.

## Philolaus

Philolaus (Φιλόλαος, Philólaos) was a Greek Pythagorean and pre-Socratic philosopher.

## Pietro Cataldi

Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Power of two

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.

## Primality test

A primality test is an algorithm for determining whether an input number is prime.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

## Prime Pages

The Prime Pages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin.

## Prime95

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.

## Primitive part and content

In algebra, the content of a polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients.

## Probable prime

In number theory, a probable prime (PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers.

## Proth number

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.

## Pseudorandom number generator

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers.

## Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.

## Ralph Ernest Powers

Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers.

## Raphael M. Robinson

Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Repunit

In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 &mdash; a more specific type of repdigit.

## Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

## Scientific American

Scientific American (informally abbreviated SciAm) is an American popular science magazine.

## Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

## Signedness

In computing, signedness is a property of data types representing numbers in computer programs.

## Solinas prime

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.

## Sophie Germain prime

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime.

## Special number field sieve

In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm.

## Speusippus

Speusippus (Σπεύσιππος; c. 408 – 339/8 BC) was an ancient Greek philosopher.

## SWAC (computer)

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.

## The New York Times

The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.

## Theon of Smyrna

Theon of Smyrna (Θέων ὁ Σμυρναῖος Theon ho Smyrnaios, gen. Θέωνος Theonos; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought.

## Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.

## Thomas John I'Anson Bromwich

Thomas John I'Anson Bromwich (1875–1929) was an English mathematician, and a Fellow of the Royal Society.

## Thymaridas

Thymaridas of Paros (Θυμαρίδας; c. 400 – c. 350 BCE) was an ancient Greek mathematician and Pythagorean noted for his work on prime numbers and simultaneous linear equations.

## Titanic prime

Titanic prime is a term coined by Samuel Yates in the 1980s, denoting a prime number of at least 1000 decimal digits.

## Tower of Hanoi

The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle.

## Trial division

Trial division is the most laborious but easiest to understand of the integer factorization algorithms.

## Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.

## Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

## Unit (ring theory)

In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.

## University of California, Los Angeles

The University of California, Los Angeles (UCLA) is a public research university in the Westwood district of Los Angeles, United States.

## University of Central Missouri

The University of Central Missouri (UCM), formerly Central Missouri State University (CMSU), is a public state university located in Warrensburg, Missouri, United States.

## University of Tennessee at Martin

The University of Tennessee at Martin (UT Martin, or UTM), located in Martin, Tennessee, in the United States, is one of the five campuses of the University of Tennessee system.

## Wagstaff prime

In number theory, a Wagstaff prime is a prime number p of the form where q is an odd prime.

## Wheat and chessboard problem

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.

## Wieferich prime

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.

## Without loss of generality

Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics.

## Woodall number

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.

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

## 127 (number)

127 (one hundred twenty-seven) is the natural number following 126 and preceding 128.

## 127 Johanna

127 Johanna is a large, dark main-belt asteroid that was discovered by French astronomers Paul Henry and Prosper Henry on November 5, 1872, and is believed to be named after Joan of Arc.

## 2,147,483,647

The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1.

## 3

3 (three) is a number, numeral, and glyph.

## 3 Juno

Juno, minor-planet designation 3 Juno in the Minor Planet Center catalogue system, is an asteroid in the asteroid belt.

## 31 (number)

31 (thirty-one) is the natural number following 30 and preceding 32.

## 31 Euphrosyne

31 Euphrosyne is the 12th-largest and the 5th-most-massive asteroid in the asteroid belt, discovered by James Ferguson on September 1, 1854.

## 7

7 (seven) is the natural number following 6 and preceding 8.

## 7 Iris

7 Iris is a large main-belt asteroid orbiting the Sun between Mars and Jupiter.

## References

Hey! We are on Facebook now! »