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Conjecture about prime numbers, proof under review
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, is the
Goldbach's_weak_conjecture
Even integers as sums of two primes
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural
Goldbach's_conjecture
German mathematician (1690–1764)
Affairs until his death in 1764. He is remembered today for Goldbach's conjecture and the Goldbach–Euler theorem. He had a close friendship with famous mathematician
Christian_Goldbach
Four basic unsolved problems about prime numbers
Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldbach's conjecture. Ivan
Landau's_problems
Theorem in number theory
can be written as a sum of three prime numbers. It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a representation
Vinogradov's_theorem
Topics referred to by the same term
mathematician Sandra Goldbach, a German rower Goldbach's conjecture, one of the oldest unsolved problems in number theory Goldbach's weak conjecture, also known
Goldbach
Prime differing from another prime by two
for example, c ln ln p . By assuming the Elliott–Halberstam conjecture or a slightly weaker version, they were able to show that there are infinitely many
Twin_prime
Number theory conjecture about odd integers
{\displaystyle n>2} . The Lemoine conjecture implies Goldbach's weak conjecture. In 2008, Zhi-Wei Sun similarly conjectured that all odd integers greater
Lemoine's_conjecture
Conjecture on zeros of the zeta function
hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's
Riemann_hypothesis
Peruvian mathematician (born 1977)
Mathématique de Jussieu, Paris. He is best known for proving Goldbach's weak conjecture. Helfgott was born on 25 November 1977 in Lima, Peru. He graduated
Harald_Helfgott
Aharoni-Korman conjecture also known as the fishbone conjecture Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Bunkbed conjecture Chinese
List_of_conjectures
from the generalized Riemann hypothesis, and (trivially) from Goldbach's weak conjecture. Schnirelmann's constant Deshouillers, J.-M.; Effinger, G.; te
Waring's prime number conjecture
Waring's_prime_number_conjecture
French mathematician
of Vinogradov's theorem, whereas the full result follows from Goldbach's weak conjecture. In turn, Ramaré's result was strengthened by Terence Tao who
Olivier_Ramaré
On mathematics of sums of prime powers
constant value? The case k = 1 {\displaystyle k=1} is a weak version of the Goldbach conjecture. Some progress has been made for k ⩽ 7 {\displaystyle k\leqslant
Waring–Goldbach_problem
Australian and American mathematician (born 1975)
Chinese: 梁蕙蘭; Jyutping: Loeng4 Wai6 Laan4 Cramer conjecture Erdős discrepancy problem Goldbach's weak conjecture Inscribed square problem "Vitae and Bibliography
Terence_Tao
integer is the sum of three primes, a close approach to proving Goldbach's weak conjecture. 1949 — Atle Selberg and Paul Erdős give the first elementary
Timeline_of_number_theory
On the distribution of prime numbers
weaker results following from twin prime conjecture and Goldbach conjecture, like Chen's theorem or the attempted proof of Goldbach's weak conjecture
Hilbert's_eighth_problem
In additive number theory, a way to measure how dense a sequence of numbers is
least 3; Goldbach's conjecture implies that this is the constant's actual value. In 2013, Harald Helfgott proved Goldbach's weak conjecture for all odd
Schnirelmann_density
Sophie Germain prime Cunningham chain Goldbach's conjecture Goldbach's weak conjecture Second Hardy–Littlewood conjecture Hardy–Littlewood circle method Schinzel's
List_of_number_theory_topics
Pre-generalisation of the fundamental lemma of sieve theory
results were superseded by Chen's theorem, and the second by Goldbach's weak conjecture ( C = 3 {\displaystyle C=3} ). Viggo Brun (1915). "Über das Goldbachsche
Brun_sieve
Mathematical conjecture about zeros of L-functions
Littlewood showed that the generalized Riemann hypothesis implies Goldbach weak conjecture for sufficiently large odd numbers. In 1997 Deshouillers, Effinger
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
Prime number of the form k*(2^n)+1
have been used to empirically verify prime-related conjectures. For example, Goldbach's weak conjecture was verified in 2008 up to 8.875 × 1030 using prime
Proth_prime
Number divisible only by 1 and itself
include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there
Prime_number
2020-03-26. "Goldbach's Conjecture Project - Detailed stats | BOINCstats/BAM!". boincstats.com. Retrieved 2020-03-28. "Goldbach's Conjecture Project - Detailed
List of volunteer computing projects
List_of_volunteer_computing_projects
Method of proof in mathematics
statement is known. One weak counterexample begins by taking some unsolved problem of mathematics, such as Goldbach's conjecture, which asks whether every
Constructive_proof
a number is prime or composite in polynomial time. A proof of Goldbach's weak conjecture was published by Harald Helfgott in 2013; as of 2025, the proof
History_of_mathematics
Exploring properties of the integers with complex analysis
and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Analytic number theory can be split up into
Analytic_number_theory
Result on density of prime numbers
still conjectures, some proven. Bertrand's postulate was proposed for applications to permutation groups. Sylvester (1814–1897) generalized the weaker statement
Bertrand's_postulate
Scottish-Jewish mathematician and philosopher (1889–1975)
number theory, including a 1963 paper comparing Lemoine's conjecture to Goldbach's weak conjecture. Levy was in the Labour Party from 1920 to 1931. He then
Hyman_Levy
Mathematical principle largely used in proof theory and constructive mathematics
an index of a proof of the Goldbach conjecture exists, then the number x is the index of a proof of the Goldbach conjecture." This is classically provable
Independence_of_premise
In mathematics, a statement that has been proven
conjecture is an unproved statement that is believed to be true. Conjectures are usually made in public, and named after their maker (e.g. Goldbach's
Theorem
23 mathematical problems stated in 1900
examples include the Weil conjectures, Paul Erdős's problems, Thurston's 24 questions, and Smale's problems. The four Weil Conjectures, made by André Weil in
Hilbert's_problems
Philosphical view that existence proofs must be constructive
even known whether either a proof or a disproof of Goldbach's conjecture must exist (the conjecture may be undecidable in traditional ZF set theory). Thus
Constructivism (philosophy of mathematics)
Constructivism_(philosophy_of_mathematics)
Ways to estimate the size of sifted sets of integers
These can be considered to be near-misses to the twin prime conjecture and the Goldbach conjecture respectively. The fundamental lemma of sieve theory, which
Sieve_theory
Type of formal logic
the other direction, Jones might say, (3) "It is possible that Goldbach's conjecture is true; but also possible that it is false", and also (4) "if it
Modal_logic
release). Retrieved 20 November 2024. Silva, Tomás Oliveira e. "Goldbach conjecture verification". Retrieved 11 April 2021. "60th Birthday of Microelectronics
Orders_of_magnitude_(numbers)
Axiomatic set theories based on the principles of mathematical constructivism
in a Π 1 0 {\displaystyle \Pi _{1}^{0}} -fashion, i.e. of Goldbach-type: Goldbach conjecture, Fermat's Last Theorem but also the Riemann hypothesis are
Constructive_set_theory
Mathematical analysis
Q(n)} . Two Π 1 0 {\displaystyle \Pi _{1}^{0}} -examples are the Goldbach conjecture and the Rosser sentence of a theory. Consider any theory T {\displaystyle
Constructive_analysis
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