Estimate of time required for prime factorization of large number

Question

I have a fairly large number, say;

189835033350996327966693308352908423562156939364642656380963289904547041916999473205569166839486951244989974581942848345682606831735428346564404270713882388199644500525024630741557243099903335030417450811633549

How can I estimate the time required (even at theoretical level) to prime factorize number like these.

Can anybody give me an approximate time needed to prime factorize this number.

thanks in advance.

EDIT

Thanks for the feedbacks.

I was trying to prime factorize this number using division method, as a trial to implement in java using bigintegers. The programs doesnt end at all!

I couldnt find a proper url where i could fit this number. Please help me with a url if any.

As I observed O(log n) time complexity can be achieved using sieve method but could not work my head around how long it would actually take to prime factor a number like this.

Answer 1

You have to specify a few more details, like what algorithms can be used. But as a rule of thumb, I'd say Wolfram Alpha can factorize any number less than $10^{200}$ in a few seconds. It might take more time to transmit the number to the Wolfram Alpha website and back than it actually takes Mathematica to carry out the computation.