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.
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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.