The name denotes a heightening of the large sieve.
The larger sieve can exploit the deletion of an arbitrary number of classes.
is a set of prime powers, N an integer,
[1] A typical application is the following result, for which the large sieve fails (specifically for
), due to Gallagher:[2] If the number of excluded residue classes modulo
The larger sieve is applied with the set
above defined to be the set of primes for which many residue classes are removed, while the large sieve is used to obtain information using the primes outside