While I am no expert in the area, nor do I know a huge amount about mathematics, wikipedia says that there are:2,220,819,602,560,918,840 primes below 10^20, which is 20 digits long. Considering that the largest known prime is almost 13 million digits long,and most of these numbers are unimaginably vast, it appears that it is not trivial to find the prime factors of a number.
For instance, If a computer can test 10 billion primes a second (which is more than a consumer grade computer can (I think)), then it would take ~2 billion seconds to go test all the primes from 2 to the 10^20. While this would be far faster on a supercomputer, if all primes up to 2^(43,112,609) â' 1 are taken into account, it is not hard to appreciate that this will take a huge amount of time.