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Goldbach's conjecture

Index Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. [1]

59 relations: Almost all, American Mathematical Society, Asian Journal of Mathematics, Asymptotic analysis, Bob Vaughan, Chen Jingrun, Chen's theorem, Christian Goldbach, Constraint (mathematics), Coprime integers, Eventually (mathematics), G. H. Hardy, Generalized Riemann hypothesis, Giuseppe Melfi, Goldbach's comet, Goldbach's weak conjecture, Greedy algorithm, Harald Helfgott, Heuristic, Hugh Lowell Montgomery, Independence (probability theory), Inequality (mathematics), Integer, Ivan Vinogradov, Johannes van der Corput, John Edensor Littlewood, Joseph-Louis Lagrange, Lagrange's four-square theorem, Lemoine's conjecture, Leonhard Euler, Lev Schnirelmann, List of unsolved problems in mathematics, Mathematician, Mathematics, Mathematische Annalen, Modular arithmetic, Natural density, Natural number, Nikolai Chudakov, Number theory, Olivier Ramaré, Parity (mathematics), Partition (number theory), Pillai sequence, Practical number, Prime number, Prime number theorem, Prime Pages, Proceedings of the USSR Academy of Sciences, Roger Heath-Brown, ..., Schnirelmann density, Semiprime, Sieve theory, Theodor Estermann, Twin prime, Uncle Petros and Goldbach's Conjecture, Waring's problem, Waring–Goldbach problem, Yuri Linnik. Expand index (9 more) »

Almost all

In mathematics, the term "almost all" means "all but a negligible amount".

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Asian Journal of Mathematics

The Asian Journal of Mathematics is a peer-reviewed scientific journal covering all areas of pure and theoretical applied mathematics.

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Asymptotic analysis

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

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Bob Vaughan

Robert Charles "Bob" Vaughan FRS (born 24 March 1945) is a British mathematician, working in the field of analytic number theory.

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Chen Jingrun

Chen Jingrun (May 22, 1933 – March 19, 1996) was a Chinese mathematician who made significant contributions to number theory.

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Chen's theorem

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes).

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Christian Goldbach

Christian Goldbach (March 18, 1690 – November 20, 1764) was a German mathematician who also studied law.

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Constraint (mathematics)

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

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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.

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Eventually (mathematics)

In the mathematical areas of number theory and analysis, an infinite sequence (a_n) is said to eventually have a certain property if all terms beyond some (finite) point in the sequence have that property.

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G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

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Generalized Riemann hypothesis

The Riemann hypothesis is one of the most important conjectures in mathematics.

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Giuseppe Melfi

Giuseppe Melfi (born in Ispica at June 11, 1967) is an Italo-Swiss mathematician.

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Goldbach's comet

Goldbach's comet is the name given to a plot of the function g(E), the so-called Goldbach function.

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Goldbach's weak conjecture

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, it would be true.

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Greedy algorithm

A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.

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Harald Helfgott

Harald Andrés Helfgott (born November 25, 1977) is a Peruvian mathematician born in Lima.

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Heuristic

A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.

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Hugh Lowell Montgomery

Hugh Lowell Montgomery (born August 26, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Inequality (mathematics)

In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).

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Integer

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

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Ivan Vinogradov

Ivan Matveevich Vinogradov (a; 14 September 1891 – 20 March 1983) (not to be confused with Askold Ivanovich Vinogradov of the Bombieri-Vinogradov theorem) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR.

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Johannes van der Corput

Johannes Gaultherus van der Corput (4 September 1890 – 16 September 1975) was a Dutch mathematician, working in the field of analytic number theory.

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John Edensor Littlewood

John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Lagrange's four-square theorem

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.

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Lemoine's conjecture

In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.

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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.

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Lev Schnirelmann

Lev Genrikhovich Schnirelmann (also Shnirelman, Shnirel'man; Лев Ге́нрихович Шнирельма́н; January 2, 1905 – September 24, 1938) was a Soviet mathematician who worked on number theory, topology and differential geometry.

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List of unsolved problems in mathematics

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.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics

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

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Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

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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).

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Natural density

In number theory, natural density (or asymptotic density or arithmetic density) is one of the possibilities to measure how large a subset of the set of natural numbers is.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Nikolai Chudakov

Nikolai Grigor'evich Chudakov (Никола́й Григо́рьевич Чудако́в; 1904–1986) was a Russian and Soviet mathematician.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Olivier Ramaré

Olivier Ramaré is a French mathematician from CNRS who works at the Aix-Marseille Université.

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Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

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Partition (number theory)

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.

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Pillai sequence

The Pillai sequence is the sequence of integers that have a record number of terms in their greedy representations as sums of prime numbers (and one).

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Practical number

In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5.

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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.

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Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

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Prime Pages

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

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Proceedings of the USSR Academy of Sciences

The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.

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Roger Heath-Brown

David Rodney "Roger" Heath-Brown FRS (born 12 October 1952), is a British mathematician working in the field of analytic number theory.

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Schnirelmann density

In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is.

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Semiprime

In mathematics, a semiprime is a natural number that is the product of two prime numbers.

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Sieve theory

Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers.

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Theodor Estermann

Theodor Estermann (5 February 1902 – 29 November 1991) was a mathematician, working in the field of analytic number theory.

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Twin prime

A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43).

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Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis.

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Waring's problem

In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers to the power of k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers.

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Waring–Goldbach problem

The Waring–Goldbach problem is a problem in additive number theory, concerning the representation of integers as sums of powers of prime numbers.

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Yuri Linnik

Yuri Vladimirovich Linnik (Ю́рий Влади́мирович Ли́нник; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.

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Redirects here:

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References

[1] https://en.wikipedia.org/wiki/Goldbach's_conjecture

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