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1. Sieve Of Eratosthenes

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   The Sieve of Eratosthenes is an ancient, deterministic algorithm used for the enumeration of prime numbers up to an arbitrary limit $N$. Developed by the Hellenistic mathematician Eratosthenes of Cyrene, the method fundamentally relies on the iterative elimination of composite numbers by marking them as multiples of their smaller prime factors. It remains a cornerstone of introductory number theory instructio…