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6 votes

What is a sieve and why are sieves useful?

The goal of sieve theory is to obtain upper and lower bounds on the cardinality of sets of the form $$S(A, \mathcal{P}, t) = \{ n \in A : \forall p \in \mathcal{P}\ (p|n \to p>t) \}$$ where $A$ is a …
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