# Brun’s constant for prime quadruplets

Brun’s constant for prime quadruplets^{} is the sum of the reciprocals of all prime quadruplets

$${B}_{4}=\sum _{\begin{array}{c}p\\ p+2\text{is prime}\\ p+6\text{is prime}\\ p+8\text{is prime}\end{array}}\left(\frac{1}{p}+\frac{1}{p+2}+\frac{1}{p+6}+\frac{1}{p+8}\right)\approx 0.8705883800.$$ |

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 for prime quadruplets |
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Canonical name | BrunsConstantForPrimeQuadruplets |

Date of creation | 2013-03-22 16:06:23 |

Last modified on | 2013-03-22 16:06:23 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11N05 |

Classification | msc 11N36 |

Synonym | Brun’s constant for prime quadruples |

Synonym | Brun’s constant for prime quartets |