Brun combinatorial sieve

E865105

analytic number theory tool combinatorial sieve number theory concept sieve method

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.

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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 NERFINISHED ⓘ large sieve inequality ⓘ
contributedTo	proof that sum of reciprocals of twin primes converges ⓘ
developedBy	Viggo Brun NERFINISHED ⓘ
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 NERFINISHED ⓘ
originCountryOfDeveloper	Norway GENERATED ⓘ
provides	lower bounds for sifted sets ⓘ upper bounds for sifted sets ⓘ
relatedTo	Brun's constant NERFINISHED ⓘ Brun's theorem NERFINISHED ⓘ Selberg sieve NERFINISHED ⓘ large sieve ⓘ sieve methods in number theory ⓘ sieve of Eratosthenes NERFINISHED ⓘ
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 ⓘ

Referenced by (1)

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Selberg sieve → contrastedWith → Brun combinatorial sieve ⓘ