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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 wikiPageExternalLink expos.html.
- Sieve_theory wikiPageID "1035915".
- Sieve_theory wikiPageRevisionID "562792873".
- Sieve_theory first "B.M.".
- Sieve_theory hasPhotoCollection Sieve_theory.
- Sieve_theory id "12559".
- Sieve_theory last "Bredikhin".
- Sieve_theory title "Sieve method".
- Sieve_theory subject Category:Sieve_theory.
- 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 "Crible (mathématiques)".
- Sieve_theory label "Sieve theory".
- Sieve_theory label "Teoria dei crivelli".
- Sieve_theory label "Teoria dos crivos".
- Sieve_theory label "Teoría de cribas".
- Sieve_theory label "نظرية الغرابيل".
- Sieve_theory label "篩法".
- Sieve_theory sameAs Teoría_de_cribas.
- Sieve_theory sameAs Crible_(mathématiques).
- Sieve_theory sameAs Teoria_dei_crivelli.
- Sieve_theory sameAs 篩法.
- Sieve_theory sameAs Teoria_dos_crivos.
- Sieve_theory sameAs m.0409st.
- Sieve_theory sameAs Q2517976.
- Sieve_theory sameAs Q2517976.
- Sieve_theory wasDerivedFrom Sieve_theory?oldid=562792873.
- Sieve_theory isPrimaryTopicOf Sieve_theory.