Selberg sieve

The Selberg sieve is a mathematical method used to estimate the number of numbers within a set that avoid certain prime factors, such as primes dividing a specific collection. It works by assigning weights to elements to effectively "filter out" those divisible by small primes, yielding an approximation of how many elements are free of these prime factors. This technique is valuable in number theory to tackle problems like finding primes or almost-primes within sequences, providing bounds and insights that otherwise would be difficult to obtain with direct counting.