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...

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...

In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular...

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...

numbers in number theory, any of a variety of methods studied in sieve theory in combinatorics, the set of methods dealt with in sieve theory or more specifically...

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...

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...

worked primarily in analytic number theory. He is the author (with Heini Halberstam) of a definitive book on sieve theory. Hans-Egon Richert was born in 1924...

In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of...

conceptual basis in number theory. It is especially suited to quick hand computation for small bounds. Whereas the sieve of Eratosthenes marks off each...

number theory, for example, sieve theory, are better covered by the second rather than the first definition: some of sieve theory, for instance, uses little...

Goldston-Pintz-Yıldırım sieve (also called GPY sieve or GPY method) is a sieve method and variant of the Selberg sieve with generalized, multidimensional sieve weights...

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...

Eduard Sievers developed a theory of the meter of Anglo-Saxon alliterative verse, which he published in his 1893 Altgermanische Metrik. Widely used by...

Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods. The convergence of the sum of reciprocals of twin primes follows...

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...

approximation) Hua's lemma Vaughan's lemma Bhaskara's lemma Fundamental lemma of sieve theory Borel–Cantelli lemma Doob–Dynkin lemma Itô's lemma (stochastic calculus)...

sieve with reduced real time expended for a given large practical sieving range. Sieve of Eratosthenes Legendre sieve Sieve of Sundaram Sieve theory A...

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes...

field sieve Large sieve Quadratic sieve Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Sieve of Pritchard Sieve, in medicine, a "surgical sieve" refers...

number theory Mahler's theorem Brun sieve Function field sieve General number field sieve Large sieve Larger sieve Quadratic sieve Selberg sieve Sieve of...

In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically...

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...

In mathematics, the sieve of Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up...

2019) was an American mathematician who pioneered large sieve theory and invented the larger sieve. Patrick Ximenes Gallagher was born on January 2, 1935...

elementary solutions Vol 2, problems 171, 173, 174 Weisstein, Eric W. "Mertens Constant". MathWorld. Varun Rajkumar, π(x) and the Sieve of Eratosthenes...

twin brothers. Iwaniec studies both sieve methods and deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic...

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...

to 1 in many programming languages. In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where...

elements. Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its...