least prime factor

The least prime factorMathworldPlanetmath of a positive integer n is the smallest positive prime numberMathworldPlanetmath dividing n. Sometimes expressed as a function, lpf(n). For example, lpf(91)=7. For a prime number p, clearly lpf(p)=p, while for any composite numberMathworldPlanetmath (except squares of primes) (lpf(n))2<n. (The function would be quite useless if 1 is considered a prime, therefore lpf(1) is undefined — though we could make an argument for lpf(0)=2). In the sequence of least prime factors for each integer in turn, each prime occurs first at the index for itself then not again until its square.

In Mathematica, one can use LeastPrimeFactor[n] after loading a number theoryMathworldPlanetmathPlanetmath package, or much more simply by using the command FactorInteger[n][[1,1]] (of course substituting n as necessary).

Title least prime factor
Canonical name LeastPrimeFactor
Date of creation 2013-03-22 17:40:03
Last modified on 2013-03-22 17:40:03
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51