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Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The primordial example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the primordial example of a sieve is the sieve of Eratosthenesthat there are infinitely many primes, One successful approach is to approximate a specific sifted set of numbers as example the set of prime number.

Really i'm interested in this question :

Question: Is it possible to prove Euclid theorem which stated that "there are infinitely many primes" using Sieve theory ?

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    You are free to [quote verbatim from the Wikipedia](https://en.m.wikipedia.org/wiki/Sieve_theory), but you should mention the source. – 2017-01-01
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    sorry for that i forgot to add wiki source , just my Goal is the definition of sieve theory , i have going to add source – 2017-01-01

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