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- Sieve theory

Brun sieve

In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are e

Sieve theory

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 prototypical example of a sifted set is the

Brun's theorem

In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually deno

Turán sieve

In number theory, the Turán sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by

Bombieri–Vinogradov theorem

In mathematics, the Bombieri–Vinogradov theorem (sometimes simply called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of prim

Legendre sieve

In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds

Fundamental lemma of sieve theory

In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richertwrite: A curious fe

Sieve of Pritchard

In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound.Like the ancient sieve of Eratosthenes, it has a simple conceptual basis in number theory.I

Sieve of Eratosthenes

In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of

Jurkat–Richert theorem

The Jurkat–Richert theorem is a mathematical theorem in sieve theory. It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture.It was proved in 1965 by Wolfgang B. Jurkat and Hans-E

Large sieve

The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to smal

Selberg sieve

In number theory, the Selberg sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed

Larger sieve

In number theory, the larger sieve is a sieve invented by Patrick X. Gallagher. The name denotes a heightening of the large sieve. Combinatorial sieves like the Selberg sieve are strongest, when only

Parity problem (sieve theory)

In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems. The problem was identified and nam

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