An elementary approach to the twin primes problem

Baier, S. (2004) An elementary approach to the twin primes problem. Monatshefte für Mathematik, 143 (4). pp. 269-283. ISSN 0026-9255

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Hardy-Littlewood [4] conjectured an asymptotic formula for the number of prime pairs (twin primes) (p, p + 2d) with p + 2d = y, where d ? N is fixed and y ? 8. Up to now, no one has been able to prove this conjecture, but employing Hardy-Littlewood's circle method, Lavrik [5] showed that in a certain sense this formula holds true for almost-all d = y/2. In the present paper, we use a completely different method to prove Lavrik's almost-all result. Our method is based on an elementary approach developed by Pan Chengdong [7] to the twin primes problem. By a slight modification of our method, we get a corresponding almost-all result for the binary Goldbach problem. From this, according to [3], we derive Vinogradov's [8] well-known Three-Primes-Theorem.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Number Theory, Ergodic Theory and Dynamical Systems (former - to 2013)
Faculty of Science > Research Groups > Number Theory (former - to 2017)
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Depositing User: Pure Connector
Date Deposited: 07 Sep 2013 05:12
Last Modified: 24 Oct 2022 04:33
DOI: 10.1007/s00605-004-0270-3

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