# Sophie Germain prime

A prime number^{} $p$ is called *Sophie Germain prime ^{}* if $2p+1$ is also prime.

The first few Sophie Germain primes are: $2,3,5,11,23,29,41,53,83,89,113,131,173,179,191,233,\mathrm{\dots}$

It is conjectured that there are infinitely many Sophie Germain primes,
but (like the Twin Prime Conjecture^{}) this has not been proven.
A heuristic estimate for the number of Sophie Germain primes less than $n$ is $\frac{2cn}{{\mathrm{ln}}^{2}n}$, where $c$ is the twin prime constant.

Title | Sophie Germain prime |
---|---|

Canonical name | SophieGermainPrime |

Date of creation | 2013-03-22 14:34:23 |

Last modified on | 2013-03-22 14:34:23 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 8 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 11A41 |

Synonym | Germain prime |