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- Sieve_theory abstract "Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The primordial example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the primordial example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve. The direct attack on prime numbers using these methods soon reaches apparently insuperable obstacles, in the way of the accumulation of error terms. In one of the major strands of number theory in the twentieth century, ways were found of avoiding some of the difficulties of a frontal attack with a naive idea of what sieving should be.One successful approach is to approximate a specific sifted set of numbers (e.g. the set ofprime numbers) by another, simpler set (e.g. the set of almost prime numbers), which is typically somewhat larger than the original set, and easier to analyze. More sophisticated sieves also do not work directly with sets per se, but instead count them according to carefully chosen weight functions on these sets (options for giving some elements of these sets more \"weight\" than others). Furthermore, in some modern applications, sieves are used not to estimate the size of a siftedset, but to produce a function that is large on the set and mostly small outside it, while being easier to analyze thanthe characteristic function of the set.".
- Sieve_theory wikiPageID "1035915".
- Sieve_theory wikiPageLength "8353".
- Sieve_theory wikiPageOutDegree "42".
- Sieve_theory wikiPageRevisionID "706861828".
- Sieve_theory wikiPageWikiLink Academic_Press.
- Sieve_theory wikiPageWikiLink Algebraic_number_theory.
- Sieve_theory wikiPageWikiLink Almost_prime.
- Sieve_theory wikiPageWikiLink American_Mathematical_Society.
- Sieve_theory wikiPageWikiLink Analytic_number_theory.
- Sieve_theory wikiPageWikiLink Annals_of_Mathematics.
- Sieve_theory wikiPageWikiLink Brun_sieve.
- Sieve_theory wikiPageWikiLink Bruns_theorem.
- Sieve_theory wikiPageWikiLink Cambridge_University_Press.
- Sieve_theory wikiPageWikiLink Category:Sieve_theory.
- Sieve_theory wikiPageWikiLink Chen_Jingrun.
- Sieve_theory wikiPageWikiLink Chens_theorem.
- Sieve_theory wikiPageWikiLink Eventually_(mathematics).
- Sieve_theory wikiPageWikiLink Friedlander–Iwaniec_theorem.
- Sieve_theory wikiPageWikiLink Fundamental_lemma_of_sieve_theory.
- Sieve_theory wikiPageWikiLink General_number_field_sieve.
- Sieve_theory wikiPageWikiLink Goldbachs_conjecture.
- Sieve_theory wikiPageWikiLink Indicator_function.
- Sieve_theory wikiPageWikiLink Integer_factorization.
- Sieve_theory wikiPageWikiLink Large_sieve.
- Sieve_theory wikiPageWikiLink Larger_sieve.
- Sieve_theory wikiPageWikiLink Legendre_sieve.
- Sieve_theory wikiPageWikiLink Number_theory.
- Sieve_theory wikiPageWikiLink Parity_problem_(sieve_theory).
- Sieve_theory wikiPageWikiLink Prime_gap.
- Sieve_theory wikiPageWikiLink Prime_number.
- Sieve_theory wikiPageWikiLink Quadratic_sieve.
- Sieve_theory wikiPageWikiLink Selberg_sieve.
- Sieve_theory wikiPageWikiLink Semiprime.
- Sieve_theory wikiPageWikiLink Sieve_of_Eratosthenes.
- Sieve_theory wikiPageWikiLink Springer_Science+Business_Media.
- Sieve_theory wikiPageWikiLink Turán_sieve.
- Sieve_theory wikiPageWikiLink Twin_prime.
- Sieve_theory wikiPageWikiLink Weight_function.
- Sieve_theory wikiPageWikiLinkText "Sieve Methods".
- Sieve_theory wikiPageWikiLinkText "Sieve theory".
- Sieve_theory wikiPageWikiLinkText "sieve method".
- Sieve_theory wikiPageWikiLinkText "sieve methods".
- Sieve_theory wikiPageWikiLinkText "sieve theory".
- Sieve_theory wikiPageWikiLinkText "sieve".
- Sieve_theory wikiPageWikiLinkText "sieves".
- Sieve_theory wikiPageWikiLinkText "sieving".
- Sieve_theory first "B.M.".
- Sieve_theory id "Sieve_method&oldid=34162".
- Sieve_theory last "Bredikhin".
- Sieve_theory title "Sieve method".
- Sieve_theory wikiPageUsesTemplate Template:Citation.
- Sieve_theory wikiPageUsesTemplate Template:Cite_book.
- Sieve_theory wikiPageUsesTemplate Template:Cite_journal.
- Sieve_theory wikiPageUsesTemplate Template:Harv.
- Sieve_theory wikiPageUsesTemplate Template:No_footnotes.
- Sieve_theory wikiPageUsesTemplate Template:SpringerEOM.
- Sieve_theory subject Category:Sieve_theory.
- Sieve_theory hypernym Set.
- Sieve_theory type Combinatoric.
- Sieve_theory comment "Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The primordial example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the primordial example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve.".
- Sieve_theory label "Sieve theory".
- Sieve_theory sameAs Q2517976.
- Sieve_theory sameAs نظرية_الغرابيل.
- Sieve_theory sameAs Teoría_de_cribas.
- Sieve_theory sameAs Sõelateooria.
- Sieve_theory sameAs Crible_(mathématiques).
- Sieve_theory sameAs Teoria_dei_crivelli.
- Sieve_theory sameAs 篩法.
- Sieve_theory sameAs Zeeftheorie.
- Sieve_theory sameAs Teoria_dos_crivos.
- Sieve_theory sameAs m.0409st.
- Sieve_theory sameAs Q2517976.
- Sieve_theory wasDerivedFrom Sieve_theory?oldid=706861828.
- Sieve_theory isPrimaryTopicOf Sieve_theory.