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# Twin prime

A **twin prime** is a prime number that differs from another prime number by two, for example the twin prime pair (41, 43).

It is not known whether there exist infinitely many twin primes. But it is known that the sum of the reciprocals of all twin primes converges to Brun's constant (about 1.902160583104).

## Count of twin prime pairs

Up to | Number of pairs |
---|---|

10^{1} |
2 |

10^{2} |
8 |

10^{3} |
35 |

10^{4} |
205 |

10^{5} |
1224 |

10^{6} |
8169 |

10^{7} |
58980 |

10^{8} |
440312 |

10^{9} |
3424506 |

10^{10} |
27412679 |

10^{11} |
224376048 |

10^{12} |
1870585220 |

10^{13} |
15834664872 |

10^{14} |
135780321665 |

10^{15} |
1177209242304 |

Reference: 'Counts of twin prime pairs and Brun's constant to 5e15' by Thomas R. Nicely [link not available anymore].

## List of twin primes

The next table includes the lower members of the first 500 twin prime pairs. The other members are found by adding 2 to the primes shown below.

**Table deleted, have to be created as upload later!**