what is the algorithm behind the factor command in linux?

Here's an example of one version of the source for GNU factor:

http://www.futuretg.com/FTHumanEvolutionCourse/Source/factor.c

It includes routines for both trial division and Pollard's rho. Looks to me on a quick scan as if it uses trial division to find some small factors (up to about lg(n)^2, which is about 4000 in this case), then Pollard if what's left isn't probably-prime. In this case that's 205432623008947 if I'm right about the 4000, i.e. 35129 * 5847949643 .

The second-largest prime factor in your example is 35129, and the square root of the largest is around 76471. So trial division alone would be fast, since it only has to try about 25 thousand candidates.

Gnu coreutils manual informs that Pollard's rho algorithm is being used.

http://www.gnu.org/software/coreutils/manual/html_node/factor-invocation.html