# rough number

A $k$-rough number^{} is an integer $n$ having only prime factors^{} greater than or equal to $k$. A number that is $k$-rough is thus not a $k$-smooth number. However, a prime $p$ is both $p$-smooth and $p$-rough because neither inequality is strict.

For example, 771166905830363 is 7-rough since, in addition to having 7 as a prime factor, it has greater primes as factors. By comparison, 93386641873154605056 is not 7-rough, and is in fact 7-smooth, since all its divisors^{} are 2, 3, and powers of those small primes.

Title | rough number |
---|---|

Canonical name | RoughNumber |

Date of creation | 2013-03-22 18:09:46 |

Last modified on | 2013-03-22 18:09:46 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 7 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A51 |

Related topic | SmoothNumber |