# rough number

A $k$- 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 RoughNumber 2013-03-22 18:09:46 2013-03-22 18:09:46 PrimeFan (13766) PrimeFan (13766) 7 PrimeFan (13766) Definition msc 11A51 SmoothNumber