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.
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| notableApplication | Brun's theorem on twin primes NERFINISHED ⓘ |
| relatedTo |
Eratosthenes sieve
ⓘ
Legendre sieve ⓘ Selberg sieve NERFINISHED ⓘ large sieve ⓘ sieve of Eratosthenes NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.