The Sieve of Atkin is an efficient algorithm used to find all prime numbers up to a specified integer. It improves upon the traditional Sieve of Eratosthenes by using a different approach that reduces the number of calculations needed. The algorithm works by marking potential prime candidates based on their remainders when divided by small integers. This sieve operates in a series of steps, first eliminating numbers that cannot be prime, then refining the list by applying specific mathematical conditions. The result is a faster method for generating prime numbers, especially useful for larger ranges compared to older sieving techniques.