# Brun’s constant

*Brun’s constant* is the sum of the reciprocals of all twin primes

$$B=\sum _{\begin{array}{c}p\\ p+2\text{is prime}\end{array}}\left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058.$$ |

Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun’s sieve (http://planetmath.org/BrunsPureSieve).

Title | Brun’s constant |
---|---|

Canonical name | BrunsConstant |

Date of creation | 2013-03-22 13:20:01 |

Last modified on | 2013-03-22 13:20:01 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 8 |

Author | bbukh (348) |

Entry type | Definition |

Classification | msc 11N36 |

Classification | msc 11N05 |

Related topic | BrunsPureSieve |