# twin prime conjecture

Two consecutive odd numbers^{} which are both prime are called twin primes^{}, e.g. 5 and 7, or 41 and 43, or 1,000,000,000,061 and 1,000,000,000,063. But is there an infinite^{} number of twin primes ?

In 1849 de Polignac made the more general conjecture that for every natural number^{} $n$, there are infinitely many prime pairs which have a distance of $2n$. The case $n=1$ is the twin prime conjecture.

In 1940, Erdős showed that there is a constant $$ and infinitely many primes $p$ such that $$ where $q$ denotes the next prime after $p$.
This result was improved in 1986 by Maier; he showed that a constant $$ can be used. The constant $c$ is called the *twin prime constant.*

In 1966, Chen Jingrun showed that there are infinitely many primes $p$ such that $p+2$ is either a prime or a semiprime.

Title | twin prime conjecture |
---|---|

Canonical name | TwinPrimeConjecture |

Date of creation | 2013-03-22 13:21:32 |

Last modified on | 2013-03-22 13:21:32 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 11 |

Author | alozano (2414) |

Entry type | Conjecture |

Classification | msc 11N05 |

Related topic | PrimeTriplesConjecture |

Related topic | BrunsConstant |

Defines | twin prime constant |

Defines | twin primes |