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Every large even number is either sum of a prime and a semi-prime or two primes
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
Chen's_theorem
Chinese number theorist
including Chen's theorem and the Chen prime. Chen was the third son in a large family from Fuzhou, Fujian, China. His father was a postal worker. Chen Jingrun
Chen_Jingrun
Sieve theory
The Jurkat–Richert theorem is a mathematical theorem in sieve theory. It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture. It
Jurkat–Richert_theorem
from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition
Monoid_factorisation
Four basic unsolved problems about prime numbers
(Vinogradov's theorem) in 1937, and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013. Chen's theorem, another weakening
Landau's_problems
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Prime number p where p+2 is prime or semiprime
Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen's theorem
Chen_prime
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Number divisible only by 1 and itself
example, Vinogradov's theorem says that every sufficiently large odd integer can be written as a sum of three primes. Chen's theorem says that every sufficiently
Prime_number
The Fulkerson–Chen–Anstee theorem is a result in graph theory, a branch of combinatorics. It provides one of two known approaches solving the digraph
Fulkerson–Chen–Anstee_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Surname list
therefore the Chinese last name Chen ranks 2nd with 88,000 and with an incidence of 1 to 900. There are 187,000 Chens in the US, as of 2014. It is the
Chen_(surname)
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Even integers as sums of two primes
primes, or a prime and a semiprime (the product of two primes). See Chen's theorem for further information. In 1975, Hugh Lowell Montgomery and Bob Vaughan
Goldbach's_conjecture
Mathematical theorem
mathematics, specifically additive number theory, Romanov's theorem is a mathematical theorem proved by Nikolai Pavlovich Romanov. It states that given
Romanov's_theorem
Chinese mathematician and politician (1910–1985)
responsible for identifying and nurturing the mathematician Chen Jingrun, who proved Chen's theorem, the best-known result on the Goldbach conjecture. Hua's
Hua_Luogeng
Hungarian mathematician (1921–1970)
of at most K {\displaystyle K} primes. Chen's theorem, a strengthening of this result, shows that the theorem is true for K = 2, for all sufficiently
Alfréd_Rényi
subsequently completed by his student Chen Jixin in 1774. Chinese remainder theorem: The Chinese remainder theorem, including simultaneous congruences in
List_of_Chinese_discoveries
Theorem about orthocenter and polars in circle geometry
Brokard's theorem (also known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. It is
Brokard's_theorem
Mathematical theorem
Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist
Linnik's_theorem
give the first elementary proof of the prime number theorem. 1966 — Chen Jingrun proves Chen's theorem, a close approach to proving the Goldbach conjecture
Timeline_of_number_theory
Product of two prime numbers
distinct ways (23 rows and 73 columns, or 73 rows and 23 columns). Chen's theorem Sphenic number, a product of three distinct primes Parity problem (sieve
Semiprime
German mathematician
Jurkat–Richert theorem, joint work with Wolfgang B. Jurkat that improved the Selberg sieve and is used in the proof of Chen's theorem. Richert also produced
Hans-Egon_Richert
Ways to estimate the size of sifted sets of integers
prime or a semiprime (the product of two primes); a closely related theorem of Chen Jingrun asserts that every sufficiently large even number is the sum
Sieve_theory
Proof assistant and programming language
Inductive Constructions), the foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source
Lean_(proof_assistant)
Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature
In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that
Chern–Gauss–Bonnet_theorem
On the distribution of prime numbers
following from twin prime conjecture and Goldbach conjecture, like Chen's theorem or the attempted proof of Goldbach's weak conjecture by Harald Helfgott
Hilbert's_eighth_problem
formulas for counting these objects in various contexts. The prime number theorem is a key result in this subject. The Mathematics Subject Classification
Multiplicative_number_theory
Long dense subsets of the integers contain arbitrarily large arithmetic progressions
In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured
Szemerédi's_theorem
Norwegian mathematician (1917–2007)
particular to providing auxiliary upper bounds, and which contributed to Chen's theorem, among other important results. In 1948, Selberg submitted two papers
Atle_Selberg
Theorem on changes in stochastic processes
Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The theorem plays a significant
Girsanov_theorem
Theorem in differential geometry
In differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying
Gauss–Bonnet_theorem
Number theory conjecture
have been attempted by many mathematicians; among them, most notably, Chen's theorem states that there exist infinitely many prime numbers n {\displaystyle
Schinzel's_hypothesis_H
free associative algebra generated by X. By the Poincaré–Birkhoff–Witt theorem it is the "same size" as the symmetric algebra of the free Lie algebra
Free_Lie_algebra
In number theory, a limitation of sieve theory
for the number of primes with some property. For example, in a sense Chen's theorem is very close to a solution of the twin prime conjecture, since it says
Parity_problem
Theorem in statistical mechanics
In statistical mechanics, the Lee–Yang theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions
Lee–Yang_theorem
Theorem in physical cosmology
The Borde–Guth–Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout
Borde–Guth–Vilenkin_theorem
When a finite set S of relations yields polynomial-time or NP-complete problems
complexity theory, a branch of computer science, Schaefer's dichotomy theorem, proved by Thomas Jerome Schaefer, states necessary and sufficient conditions
Schaefer's_dichotomy_theorem
Chinese-American mathematician (born 1962)
become interested in number theory after reading about Chen Jingrun's proof of Chen's theorem which made substantial progress on Goldbach's conjecture
Shou-Wu_Zhang
East Asian ethnic group
purely conformational change. Mathematics genius, Chen Jingrun invented the Chen's theorem and Chen prime, he also stunned famous mathematicians by providing
Fuzhou_people
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces:
Uniformization_theorem
Province in South China
engineer of Mongolian origin Chen Jingrun (1933–1996), a widely known mathematician who invented the Chen's theorem and Chen prime Wang Wen-hsing (born
Fujian
quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle
Landau–Yang_theorem
Pre-generalisation of the fundamental lemma of sieve theory
product of at most 9 primes. The last two results were superseded by Chen's theorem, and the second by Goldbach's weak conjecture ( C = 3 {\displaystyle
Brun_sieve
Mathematics used in Ancient China
either two primes, or a prime and a semiprime, which is now called Chen's theorem. His work was important for research of Goldbach's conjecture. In 1949
Chinese_mathematics
Method in probability theory
known proofs of a specific central limit theorem, Charles Stein developed a new way of proving the theorem for his statistics lecture. His seminal paper
Stein's_method
Theorem in integral geometry
integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in R n . {\displaystyle \mathbb
Hadwiger's_theorem
Description of degree sequences of graphs
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph
Erdős–Gallai_theorem
Theorem in quantum mechanics
\Phi _{0}=hc/e} (the magnetic flux quantum). The theorem was first stated and proven by Nina Byers and Chen-Ning Yang (1961), and further developed by Felix
Byers–Yang_theorem
Theorem of dynamical systems
The Liouville–Arnold theorem is a result in classical mechanics which says, roughly speaking, that seemingly complicated systems can be described as combinations
Liouville–Arnold_theorem
Graph that can be embedded in the plane
conditions hold for v ≥ 3: Theorem 1. e ≤ 3v − 6; Theorem 2. If there are no cycles of length 3, then e ≤ 2v − 4. Theorem 3. f ≤ 2v − 4. In this sense
Planar_graph
Theorem in order and lattice theory
the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:
Knaster–Tarski_theorem
Theorem on equilateral triangles
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral
Viviani's_theorem
Result on density of prime numbers
and so it is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with π ( x )
Bertrand's_postulate
field of limit analysis is based on a set of theorems, referred to as limit theorems, which are a set of theorems based on the law of conservation of energy
Limit_analysis
Relation between frequency- and time-domain behavior at large time
In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain
Final_value_theorem
Chinese writer
Conjecture (哥德巴赫猜想), a biography of the mathematician Chen Jingrun, who had proved Chen's theorem despite being persecuted during the Cultural Revolution
Xu_Chi
The importance of the Theorem of Miquel shows in the following theorem, which is due to v. d. Waerden, Smid and Chen: Theorem: Only a Laguerre plane
Laguerre_plane
Existence of a line through two points
The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the
Sylvester–Gallai_theorem
Quadratic imaginary number fields with unique factorisation
In number theory, the Heegner theorem or Stark-Heegner theorem establishes the complete list of the quadratic imaginary number fields whose rings of integers
Stark–Heegner_theorem
Theorem in graph theory
The Gale–Ryser theorem is a result in graph theory and combinatorial matrix theory, two branches of combinatorics. It provides one of two known approaches
Gale–Ryser_theorem
Plastic limit theorems in continuum mechanics provide two bounds that can be used to determine whether material failure is possible by means of plastic
Plastic_limit_theorems
fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Continuous fixed-point theorems often require
Discrete_fixed-point_theorem
Theorem about inscribed and circumscribed circles
In geometry, the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters
Incenter–excenter_lemma
Mathematical theorem
In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower
Bloch's theorem (complex analysis)
Bloch's_theorem_(complex_analysis)
Chinese American mathematician
Chang's model are named after him. He also proved the ordinal partition theorem (expressed in the arrow notation for Ramsey theory) ωω→(ωω,3)2, originally
Chen_Chung_Chang
Analysis of datasets using techniques from topology
first classification theorem for persistent homology appeared in 1994 via Barannikov's canonical forms. The classification theorem interpreting persistence
Topological_data_analysis
Graph-theoretic description of polyhedra
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices
Steinitz's_theorem
Theorem on edge-disjoint spanning trees
In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests)
Nash-Williams_theorem
at mid-ocean ridges. The Fabius function is published. Chen Jingrun publishes Chen's theorem: every sufficiently large even number can be written as
1966_in_science
Theorem in mathematical logic
In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the
Lindström's_theorem
Mathematical problem in number theory
whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its own Mathematics
Waring's_problem
Result concerning the holomorphic extensions In several complex variables
(2011) "Hörmander's L2－estimate and the Ohsawa-Takegoshi extension theorem by Bo-Yong Chen Young mathematician workshop on SCV July 24-July 27, 2013, Nagoya"
Ohsawa–Takegoshi L2 extension theorem
Ohsawa–Takegoshi_L2_extension_theorem
Theorem that the sum of the reciprocals of the twin primes converges
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes converges to a finite value known as Brun's constant. While
Brun's_theorem
Graph coloring with equal color classes
any number of colors greater than or equal to k. The Hajnal–Szemerédi theorem, posed as a conjecture by Paul Erdős (1964) and proven by András Hajnal
Equitable_coloring
Chinese-American physicist (1922–2025)
(1952): for his works with Lee on the Lee–Yang theory and the Lee–Yang theorem, which describe the liquid-gas phase transition based on microscopic properties
Yang_Chen-Ning
Hypothesis about intelligent agents
Russell, Stuart (2017-06-15). "The Off-Switch Game". arXiv:1611.08219 [cs.AI]. Chen, Angela (11 September 2014). "Is Artificial Intelligence a Threat?". The
Instrumental_convergence
Bound on probability of a random variable being far from its mean
(the square root of the variance). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics
Chebyshev's_inequality
Type of artificial neural network architecture
architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs),
Kolmogorov–Arnold_Networks
Prime differing from another prime by two
reciprocals of the twin primes was convergent. This famous result, called Brun's theorem, was the first use of the Brun sieve and helped initiate the development
Twin_prime
Mathematical result in the theory of Sobolev spaces
In mathematics, the Aubin–Lions lemma (or theorem) is the result in the theory of Sobolev spaces of Banach space-valued functions, which provides a compactness
Aubin–Lions_lemma
Theory of stochastic processes
processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem states that a stochastic
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Topological theorem
mathematical field of differential geometry, the Osserman–Xavier–Fujimoto theorem concerns the Gauss maps of minimal surfaces in the three-dimensional Euclidean
Osserman–Xavier–Fujimoto theorem
Osserman–Xavier–Fujimoto_theorem
Calculus of vector-valued functions
corresponding theorems which generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce
Vector_calculus
Taiwanese mathematician alleged to have been murdered by KMT
451–464. doi:10.1214/aop/1176994720. ISSN 0091-1798. Chen, Wen Chen (1981-12-01). "Some local limit theorems in the symmetric Dirichlet-Multinomial urn models"
Chen_Wen-chen
History Faculty at the University of Oxford 25 October 2012 Fermat's Last Theorem Marcus du Sautoy, Professor of Mathematics & Simonyi Professor for the
List of In Our Time programmes
List_of_In_Our_Time_programmes
Problem that attempts to explain why cats fall on their feet
Falling Felines and Fundamental Physics. New Haven London: Yale University Press. ISBN 978-0-300-23129-8. Lagrangian Reduction and the Falling Cat Theorem
Falling_cat_problem
Q-analog of hypergeometric series
_{k=1}^{N}\left(1+yq^{k}\right)} of the q-binomial theorem (also sometimes known as the Cauchy binomial theorem). Here [ N n ] q {\displaystyle
Basic_hypergeometric_series
Probability distribution
unbiased and uniformly with minimum variance, proven using Lehmann–Scheffé theorem, since it is based on a minimal sufficient and complete statistic (that
Binomial_distribution
Physics problem related to laws of motion and gravity
bounded away from a triple collision. This implies, by Cauchy's existence theorem for differential equations, that there are no complex singularities in
Three-body_problem
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is widely used to model and solve
Mathematics
Method of evaluating certain integrals along paths in the complex plane
application of the Cauchy integral formula or residue theorem is possible application of Cauchy's integral theorem The integral is reduced to only an integration
Contour_integration
Type of theory in mathematical logic
model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of stating that if a first-order theory in a countable language is
Categorical_theory
Conjecture in number theory
amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof
Beal_conjecture
Chinese-American mathematician (born 1949)
partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors
Shing-Tung_Yau
Shape with four equal sides and angles
number of equal-area triangles, a result of Monsky's theorem. Cross's theorem or Vecten's theorem states that, for a triangle formed by the sides of three
Square
Conjecture in number theory
smaller than c {\displaystyle c} . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its
Abc_conjecture
On centroids of sets of lattice points
Reiher proved the full conjecture using the Chevalley–Warning theorem. Savchev, S.; Chen, F. (2005). "Kemnitz' conjecture revisited". Discrete Mathematics
Kemnitz's_conjecture
Field in mathematics similar to the real numbers
fields of hyperreal numbers that include infinitesimals. In algebra, most theorems that involve the real numbers remain true when formulated for arbitrary
Real_closed_field
Type of polynomial used in Numerical Analysis
by Bernstein in a constructive proof of the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted
Bernstein_polynomial
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CHENS THEOREM
CHENS THEOREM
CHENS THEOREM
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CHENS THEOREM
CHENS THEOREM
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