Sieve theory

Sieve theory, in mathematics, is a method used primarily in number theory to identify or filter numbers based on certain properties. It works by "sieving" through a set of numbers, much like a sieve separates smaller particles from larger ones. For example, to find prime numbers, one could remove multiples of known primes from a list of numbers. This process helps mathematicians understand the distribution of numbers and identify patterns, aiding in problems like estimating the density of prime numbers or finding specific types of integers with desired characteristics.