For a finite integer set and a set of primes , the sifting function counts elements of divisible by no prime in below :
An upper-bound sieve bounds the size of a sifted set from above. In a dimension-one problem with one forbidden class modulo each relevant prime , its main density factor is comparable to .
If three nonproportional linear forms exclude three distinct residue classes modulo every sufficiently large prime, the upper-bound sieve has dimension three and gives an upper bound of order .
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Sieve theory is a branch of number theory that involves the use of combinatorial methods to count or estimate the size of sets of integers, particularly with respect to divisibility conditions. It is often used to study the distribution of primes and other arithmetic functions. The basic idea is to "sieve" out unwanted elements from a set, such as all multiples of a certain integer, in order to isolate the primes or other numbers of interest.