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Sieves
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Sieves are algorithms to cull out numbers of a specific type from a larger set of numbers. Perhaps the most famous sieve is the sieve of Eratosthenes, which culls the prime numbers out from an array that also includes composite numbers (and often also 1, rarely 0). The Eratosthenes sieve is easy to explain and easy to implement, but even with optimizations is rather inefficient for larger prime numbers. More sophisticated sieves include quadratic sieves and probabilistic sieves. See also sieve of Atkin.