Brun sieve
E865103
The Brun sieve is a combinatorial method in analytic number theory, developed by Viggo Brun, used to estimate the distribution of prime numbers and almost-primes in various sequences.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Brun sieve canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10462061 — 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: Brun sieve Context triple: [Selberg sieve, relatedTo, Brun sieve]
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A.
Selberg sieve
The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
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B.
Trial Division
The Trial Division is the branch of the International Criminal Court responsible for conducting trials and determining the guilt or innocence of accused individuals in cases of serious international crimes.
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C.
Trial Division
The Trial Division is a unit within the New York County District Attorney’s Office responsible for prosecuting criminal cases in court from arraignment through verdict.
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D.
Trial Division
The Trial Division is the primary branch of the High Court of American Samoa responsible for hearing and deciding civil and criminal cases at first instance.
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E.
Atkin
Atkin is an English surname, typically derived as a diminutive or pet form of the given name Adam.
- 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: Brun sieve Target entity description: The Brun sieve is a combinatorial method in analytic number theory, developed by Viggo Brun, used to estimate the distribution of prime numbers and almost-primes in various sequences.
-
A.
Selberg sieve
The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
-
B.
Trial Division
The Trial Division is the branch of the International Criminal Court responsible for conducting trials and determining the guilt or innocence of accused individuals in cases of serious international crimes.
-
C.
Trial Division
The Trial Division is a unit within the New York County District Attorney’s Office responsible for prosecuting criminal cases in court from arraignment through verdict.
-
D.
Trial Division
The Trial Division is the primary branch of the High Court of American Samoa responsible for hearing and deciding civil and criminal cases at first instance.
-
E.
Atkin
Atkin is an English surname, typically derived as a diminutive or pet form of the given name Adam.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial sieve
ⓘ
method in analytic number theory ⓘ sieve method ⓘ |
| appliesTo |
sequences defined by congruence conditions
ⓘ
sets of integers with multiplicative constraints ⓘ |
| approximateDate | 1910s ⓘ |
| basedOn | combinatorial inclusion–exclusion ⓘ |
| developedBy | Viggo Brun ⓘ |
| field |
analytic number theory
ⓘ
number theory ⓘ |
| generalizes | classical combinatorial sieves ⓘ |
| hasConcept |
lower bound sieve
ⓘ
sieve weight ⓘ sifted set ⓘ sifting density ⓘ upper bound sieve ⓘ |
| hasLimitation |
cannot by itself prove infinitude of twin primes
ⓘ
gives relatively weak error terms compared to later sieves ⓘ |
| hasProperty |
gives upper and lower bounds rather than exact counts
ⓘ
non-constructive with respect to explicit primes ⓘ |
| historicalSignificance |
first effective combinatorial sieve for twin primes
ⓘ
pioneered systematic use of combinatorial sieves in prime distribution ⓘ |
| implies | convergence of sum of reciprocals of twin primes ⓘ |
| influenced | modern sieve theory ⓘ |
| mathematicsSubjectClassification | 11N35 ⓘ |
| namedAfter | Viggo Brun ⓘ |
| notableApplication | Brun's theorem on twin primes ⓘ |
| relatedTo |
Eratosthenes sieve
ⓘ
Legendre sieve ⓘ Selberg sieve ⓘ large sieve ⓘ sieve of Eratosthenes ⓘ |
| usedFor |
bounding number of integers free of small prime factors
ⓘ
estimating distribution of almost-primes ⓘ estimating distribution of prime numbers ⓘ problems about prime constellations ⓘ problems about twin primes ⓘ sieve-theoretic estimates in arithmetic progressions ⓘ |
| usedIn |
additive problems involving primes
ⓘ
distribution of prime factors of integers ⓘ problems on gaps between primes ⓘ study of almost-prime values of polynomials ⓘ |
| usesTool |
Möbius function
ⓘ
estimates for multiplicative functions ⓘ inclusion–exclusion principle ⓘ |
| yearIntroduced | early 20th century ⓘ |
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: Brun sieve Description of subject: The Brun sieve is a combinatorial method in analytic number theory, developed by Viggo Brun, used to estimate the distribution of prime numbers and almost-primes in various sequences.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.