I need 2-3 pages written about the sieve of Eratosthenes. Starting from the Eratosthenes-legendre sieve going to Eratosthenes general sieve, while giving some detailed formulas and explanations for each, using some lemma and examples. And finishing with some applications.

The work has to be authentic and original (not copied), with the references stated where its used on the paper and at the end

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