Goldbach conjecture
E451524
The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Goldbach conjecture canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T4552365 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Goldbach conjecture Context triple: [Hardy–Littlewood circle method, appliedTo, Goldbach conjecture]
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A.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
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B.
Hardy–Littlewood conjectures
The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
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C.
Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
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D.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
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E.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Goldbach conjecture Target entity description: The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
-
A.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
-
B.
Hardy–Littlewood conjectures
The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
-
C.
Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
-
D.
Hilbert–Pólya conjecture
The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
-
E.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
unsolved problem in number theory ⓘ |
| alsoKnownAs | strong Goldbach conjecture NERFINISHED ⓘ |
| appearsIn | many introductory texts on analytic number theory ⓘ |
| communicatedTo | Leonhard Euler NERFINISHED ⓘ |
| conjecturesThat | every even integer greater than 2 is the sum of two prime numbers ⓘ |
| connectedConcept |
Goldbach function
NERFINISHED
ⓘ
Goldbach partition NERFINISHED ⓘ |
| difficulty | one of the oldest unsolved problems in mathematics ⓘ |
| field | number theory ⓘ |
| hasApproximateResult |
every sufficiently large even integer is the sum of a prime and a number with at most two prime factors
ⓘ
every sufficiently large even integer is the sum of two primes or almost primes ⓘ |
| hasConsequence | infinitely many Goldbach partitions for each even integer if true ⓘ |
| hasVariant |
binary Goldbach conjecture
NERFINISHED
ⓘ
ternary Goldbach conjecture NERFINISHED ⓘ |
| impliedBy | Generalized Riemann Hypothesis (for certain conditional results) NERFINISHED ⓘ |
| implies | every sufficiently large even integer is the sum of two primes ⓘ |
| isPartOf |
Hilbert problems (informally related but not one of them)
ⓘ
Landau problems NERFINISHED ⓘ |
| logicalForm | for all even n > 2, there exist primes p and q such that n = p + q ⓘ |
| majorContributor |
Chen Jingrun
NERFINISHED
ⓘ
G. H. Hardy NERFINISHED ⓘ Ivan Vinogradov NERFINISHED ⓘ J. E. Littlewood NERFINISHED ⓘ |
| mentionedIn | letter from Christian Goldbach to Leonhard Euler NERFINISHED ⓘ |
| modernFormulation | every even integer greater than 2 is the sum of two primes ⓘ |
| modernFormulationBy | Leonhard Euler NERFINISHED ⓘ |
| namedAfter | Christian Goldbach NERFINISHED ⓘ |
| openAsOf | 2024 ⓘ |
| originalFormulation | every integer greater than 5 is the sum of three primes ⓘ |
| provedForSpecialCase | ternary Goldbach conjecture proved by Harald Helfgott ⓘ |
| quantificationDomain | even integers greater than 2 ⓘ |
| relatedConjecture | weak Goldbach conjecture NERFINISHED ⓘ |
| relatedTo |
Riemann Hypothesis
NERFINISHED
ⓘ
circle method ⓘ distribution of prime numbers ⓘ sieve methods ⓘ |
| statedBy | Christian Goldbach NERFINISHED ⓘ |
| status |
open problem
ⓘ
unproven ⓘ |
| subfield | additive number theory ⓘ |
| typeOfStatement | universal statement about even integers ⓘ |
| usesConcept | prime numbers ⓘ |
| verifiedByComputationUpTo | very large bounds (e.g., at least 4·10^18 as of early 21st century) ⓘ |
| yearProposed | 1742 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Goldbach conjecture Description of subject: The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.