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

## Abstract

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 |
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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) |

Related URLs: | |

Depositing User: | Pure Connector |

Date Deposited: | 07 Sep 2013 05:12 |

Last Modified: | 24 Oct 2022 04:33 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/43190 |

DOI: | 10.1007/s00605-004-0270-3 |

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