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The prime number theorem via the large sieve
Published online by Cambridge University Press: 26 February 2010
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In the last three decades there appeared a number of elementary proofs of the prime number theorem (PNT) in the literature (see [3] for a survey). Most of these proofs are based, at least in part, on ideas from the original proof by Erdős [5] and Selberg [12]. In particular, one of the main ingredients of the Erdős-Selberg proof, Selberg's formula
(where p and q run through primes) appears, in some form, in almost all these proofs.
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