twin prime conjecture
E451529
The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
All labels observed (1)
| Label | Occurrences |
|---|---|
| twin prime conjecture canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4552479 — 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: twin prime conjecture Context triple: [Hardy–Littlewood conjectures, relatedTo, twin prime conjecture]
-
A.
prime number theorem
The prime number theorem is a fundamental result in number theory that describes how prime numbers become less frequent and provides an approximate formula for the number of primes less than a given large number.
-
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.
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.
-
D.
Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
-
E.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
- 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: twin prime conjecture Target entity description: The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
-
A.
prime number theorem
The prime number theorem is a fundamental result in number theory that describes how prime numbers become less frequent and provides an approximate formula for the number of primes less than a given large number.
-
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.
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.
-
D.
Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
-
E.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
unsolved problem in number theory ⓘ |
| consequenceIfTrue |
infinitely many primes p such that p and p+2 are both prime
ⓘ
there are infinitely many prime gaps equal to 2 ⓘ |
| difficulty | unsolved for more than a century ⓘ |
| doesNotClaim |
density of twin primes
ⓘ
formula for twin primes ⓘ |
| field | number theory ⓘ |
| historicalAttribution |
often attributed to Alphonse de Polignac
ⓘ
studied by Atle Selberg NERFINISHED ⓘ studied by G. H. Hardy NERFINISHED ⓘ studied by J. E. Littlewood NERFINISHED ⓘ studied by James Maynard ⓘ studied by Paul Erdős ⓘ studied by Terence Tao NERFINISHED ⓘ studied by Viggo Brun NERFINISHED ⓘ studied by Yitang Zhang ⓘ |
| implies | existence of infinitely many twin prime pairs (p,p+2) ⓘ |
| involvesConcept |
infinite set
ⓘ
prime gaps ⓘ prime number ⓘ twin primes ⓘ |
| knownEvidence |
heuristic support from Hardy–Littlewood k-tuple conjecture
ⓘ
numerical verification for very large ranges of integers ⓘ probabilistic models of primes suggest infinitude of twin primes ⓘ |
| openQuestion |
exact distribution of twin primes
ⓘ
whether there are infinitely many twin primes ⓘ |
| relatedConcept |
Brun sieve
ⓘ
Brun's constant NERFINISHED ⓘ |
| relatedConjecture |
Goldbach conjecture
NERFINISHED
ⓘ
Hardy–Littlewood prime k-tuple conjecture NERFINISHED ⓘ Polignac's conjecture NERFINISHED ⓘ prime k-tuple conjecture NERFINISHED ⓘ |
| relatedResult |
Brun proved convergence of the sum of reciprocals of twin primes
NERFINISHED
ⓘ
Hardy–Littlewood conjectured an asymptotic formula for twin primes ⓘ Maynard–Tao method improved bounds on prime gaps ⓘ Zhang proved bounded gaps between primes ⓘ bounded gaps between primes theorem ⓘ |
| relatedSequence | sequence of twin primes (3,5),(5,7),(11,13),(17,19),... ⓘ |
| specialCaseOf | Polignac's conjecture NERFINISHED ⓘ |
| statement | there exist infinitely many pairs of prime numbers that differ by 2 ⓘ |
| status | open ⓘ |
| subfield |
analytic number theory
ⓘ
prime number theory ⓘ |
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: twin prime conjecture Description of subject: The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.