Molu wrote:
That would be *very* few. Only those who have access
to water-cooled mainframes they can use for personal purposes. Numbers which are
factorised now are immensely huge, far beyond the capability of Windows Calculator. I
think posting a factorisation of such a number without sources would have to be deleted as
not being reasonably verifiable.
molu
No, multiplication of large numbers is actually very fast, particularly
if you use FFT-based algorithms.
In most cases of practically factorizable numbers, even this is not
necessary. For example, I can multiply
16347336458092538484431338838650908598417836700330
92312181110852389333100104508151212118167511579
by
1900871281664822113126851573935413975471896789968
515493666638539088027103802104498957191261465571
to get
RSA-640 =
3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609
in a tiny fraction of a second, using Python as a bignum calculator on a
bog-standard uniprocessor CPU.
Now, _factoring_ it is a different matter: that took 5 CPU-years using
30 2.2 GHz Opteron CPUs in late 2005. See
http://www.loria.fr/~zimmerma/records/factor.html and
http://www.rsasecurity.com/rsalabs/node.asp?id=2093 for more background.
-- Neil