# One of the factors greater than $x$

Is there an easy way to tell Mathematica to find one of the prime factors of $n$ greater than $x$. For example, if $n=1299709\cdot 7919 \cdot 17$, is there a way to request a factor greater than $100$. Please note that I am not interested in finding all factors and filtering the result. My question is about stopping the algorithm as soon as a factor greater than $x$ is found.

Edit: If that capability is not built-in, is there a way to stop the factorization process as soon as one factor is found? There is no assumption about one of the factors being small.

FactorInteger starts with trial division and then moves to Pollard methods, ECM, and MPQS. In principle several of those can deliver a nonprime factor. When the optional second argument is set, I'm not sure if any factor is guaranteed to be prime. – Daniel Lichtblau Sep 30 '14 at 19:11

• FactorInteger[n, k] will stop after k different factors were found – Dr. belisarius Sep 30 '14 at 17:32
• Thanks. That definitely answers the edited question. – user11356 Sep 30 '14 at 17:33
• It actually answers the question entirely since one of the factors in FactorInteger[n,2] is greater than $x$. – user11356 Sep 30 '14 at 17:45

• FactorInteger starts with trial division and then moves to Pollard methods, ECM, and MPQS. In principle several of those can deliver a nonprime factor. When the optional second argument is set, I'm not sure if any factor is guaranteed to be prime. – Daniel Lichtblau Sep 30 '14 at 19:11