# probable prime

A sufficiently large odd integer $q$ believed to be a prime number^{} because it has passed some preliminary primality test relative to a given base, or a pattern suggests it might be prime, but it has not yet been subjected to a conclusive primality test.

For primes with no specific form, it is required to test every potential prime factor^{} $$ to be absolutely sure that $q$ is in fact a prime. For Mersenne probable primes^{}, the Lucas-Lehmer test is accepted as a conclusive primality test.

Once a probable prime is conclusively shown to be a prime, it of course loses the label ”probable.” It also loses it if conclusively shown to be composite, but in that case it might then be called a pseudoprime^{} (http://planetmath.org/PseudoprimeP) relative to base $a$.

Title | probable prime |
---|---|

Canonical name | ProbablePrime |

Date of creation | 2013-03-22 15:53:46 |

Last modified on | 2013-03-22 15:53:46 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |