In mathematics, the large sieve is a method (or family of methods and related ideas) in analytic number theory.
Its name comes from its original application: given a set such that the elements of S are forbidden to lie in a set Ap ⊂ Z/p Z modulo every prime p, how large can S be? Here Ap is thought of as being large, i.e., at least as large as a constant times p; if this is not the case, we speak of a small sieve. (The term "sieve" is seen as alluding to, say, sifting ore for gold: we "sift out" the integers falling in one of the forbidden congruence classes modulo p, and ask ourselves how much is left at the end.)
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Famous quotes containing the words large and/or sieve:
“In our large cities, the population is godless, materialized,—no bond, no fellow-feeling, no enthusiasm. These are not men, but hungers, thirsts, fevers, and appetites walking. How is it people manage to live on,—so aimless as they are? After their peppercorn aims are gained, it seems as if the lime in their bones alone held them together, and not any worthy purpose.”
—Ralph Waldo Emerson (1803–1882)
“It’s like pushing marbles through a sieve. It means the sieve will never be the same again.”
—Before the 1972 Democratic Convention in Miami. As quoted in Crazy Salad, ch. 6, by Nora Ephron (1972)