Brun combinatorial sieve
E865105
The Brun combinatorial sieve is a classical number-theoretic sieving method, developed by Viggo Brun, that uses combinatorial techniques to estimate the distribution of integers free of small prime factors and was historically applied to problems like twin primes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Brun combinatorial sieve canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10462078 — 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 combinatorial sieve Context triple: [Selberg sieve, contrastedWith, Brun combinatorial sieve]
-
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.
Selberg–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
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C.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
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D.
Turán–Kubilius inequality
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
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E.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
- 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 combinatorial sieve Target entity description: The Brun combinatorial sieve is a classical number-theoretic sieving method, developed by Viggo Brun, that uses combinatorial techniques to estimate the distribution of integers free of small prime factors and was historically applied to problems like twin primes.
-
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.
Selberg–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
-
C.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
D.
Turán–Kubilius inequality
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
-
E.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
analytic number theory tool
ⓘ
combinatorial sieve ⓘ number theory concept ⓘ sieve method ⓘ |
| aimsToEstimate |
density of sifted sets of integers
ⓘ
distribution of integers free of small prime factors ⓘ |
| appliedTo |
distribution of almost primes
ⓘ
integers without small prime factors ⓘ twin prime problem ⓘ |
| assumes | estimates for sums over primes ⓘ |
| belongsTo | classical sieve methods ⓘ |
| category | mathematical method ⓘ |
| contrastsWith |
Selberg sieve
ⓘ
large sieve inequality ⓘ |
| contributedTo | proof that sum of reciprocals of twin primes converges ⓘ |
| developedBy | Viggo Brun ⓘ |
| developedInCentury | 20th century ⓘ |
| field |
analytic number theory
ⓘ
number theory ⓘ |
| focusesOn | integers free of small prime divisors ⓘ |
| framework | combinatorial sieving of sets of integers ⓘ |
| historicalSignificance | first effective combinatorial sieve for twin primes ⓘ |
| influenced | modern sieve theory ⓘ |
| languageOfOriginalWork | Norwegian ⓘ |
| namedAfter | Viggo Brun ⓘ |
| originCountryOfDeveloper | Norway ⓘ |
| provides |
lower bounds for sifted sets
ⓘ
upper bounds for sifted sets ⓘ |
| relatedTo |
Brun's constant
ⓘ
Brun's theorem ⓘ Selberg sieve ⓘ large sieve ⓘ sieve methods in number theory ⓘ sieve of Eratosthenes ⓘ |
| studies | integers with restricted prime factors ⓘ |
| typicalInput | set of integers with arithmetic structure ⓘ |
| typicalOutput | bounds on size of sifted subset ⓘ |
| usedFor |
bounding number of almost primes up to x
ⓘ
bounding number of twin primes up to x ⓘ |
| usedIn |
additive number theory
ⓘ
multiplicative number theory ⓘ |
| uses |
combinatorial techniques
ⓘ
inclusion–exclusion principle ⓘ |
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
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Input
Subject: Brun combinatorial sieve Description of subject: The Brun combinatorial sieve is a classical number-theoretic sieving method, developed by Viggo Brun, that uses combinatorial techniques to estimate the distribution of integers free of small prime factors and was historically applied to problems like twin primes.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.