# Goldbach’s conjecture

The conjecture states that every even integer $n>2$ is expressible as the sum of two primes.

In 1966 Chen proved that every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime divisors^{}.

Vinogradov proved that every sufficiently large *odd* number is a sum of three primes. In 1997 it was shown by J.-M. Deshouillers, G. Effinger, H. Te Riele, and D. Zinoviev that, assuming a generalized Riemann hypothesis^{}, every odd number^{} $n>5$ can be represented as sum of three primes.

The conjecture was first proposed in a 1742 letter from Christian Goldbach to Euler and still remains unproved.

Title | Goldbach’s conjecture |
---|---|

Canonical name | GoldbachsConjecture |

Date of creation | 2013-03-22 12:13:43 |

Last modified on | 2013-03-22 12:13:43 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 11 |

Author | drini (3) |

Entry type | Conjecture |

Classification | msc 11P32 |

Classification | msc 11-00 |

Related topic | Prime |