## The Goldbach ConjectureThis book provides a detailed description of a most important unsolved mathematical problem OCo the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920''s. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture." |

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### Contents

I | 1 |

II | 19 |

III | 21 |

IV | 61 |

V | 65 |

VI | 72 |

VII | 81 |

VIII | 91 |

XIV | 161 |

XV | 166 |

XVI | 183 |

XVII | 185 |

XVIII | 192 |

XIX | 214 |

XX | 227 |

XXI | 238 |

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### Common terms and phrases

Acta Arith Acta Math Akad applications arithmetical progression Atle Selberg Bombieri Brun character mod deduce denote the number density Dirichlet L-series Dokl estimation function G. H. Hardy Goldbach conjecture Goldbach problem Hardy and J. E. Hardy and Littlewood Hence I. M. Vinogradov inequality interval J. E. Littlewood L-function Landau large even integer large sieve Lemma Linnik logx London Math mean value theorem mod q Nauk SSSR number of elements number of prime number of zeros obtain odd number odd primes Pan Cheng Dong paper Partitio numerorum positive integer positive number prime divisors prime factors prime number theory primitive character Proc proof of Theorem R. C. VAUGHAN Renyi representation of large result Riemann hypothesis Sbornik Selberg sieve method sieve of Eratosthenes Sinica square free sum of primes sum of three three primes theorem Viggo Brun Wang Yuan