I don't work for the NSA—I just have a laptop, and a copy of Mathematica. The factorization took about 10 seconds.
Mathematica is really a pretty remarkable piece of software. I doubt it's world class for factorization, but it gives you easy access to a lot of pretty darn good algorithms for a wide range of problems.
There's 1 sentence on the implementation of FactorInteger in the docs, FWIW:
OK, so take a 64 bit integer. That's the typical size of an integer in a modern programming language. A signed integer can represent 2^63-1 which is 9223372036854775807.
Imagine a "big integer" which is a composite of multiple 64-bit integers. With a big integer made up of two regular integers, you can represent the value 170141183460469231731687303715884105727. With three, you get to 3138550867693340381917894711603833208051177722232017256447 if I'm doing the math right. That's already in the ballpark of the number you mentioned - just three regular integers together.
Granted, I'm not talking about how difficult the factoring is, but it's worth noting that the size of the numbers are pretty small to a computer. Modern computers are really fast and can brute force a large number of computations. Mathematica probably has a fairly optimized general purpose factoring algorithm as well.
A number like this might be more difficult to factor:
Mathematica is really a pretty remarkable piece of software. I doubt it's world class for factorization, but it gives you easy access to a lot of pretty darn good algorithms for a wide range of problems.
There's 1 sentence on the implementation of FactorInteger in the docs, FWIW:
http://reference.wolfram.com/language/tutorial/SomeNotesOnIn...