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If one should attempt to factorize a number like the RSA-2048, or in general any number with $n$ decimal digits, using the best algorithm available and a modern desktop PC, what is the approximate length in time it would take (as a function of $n$) ? I'd like a general formula (possible parameterized with CPU speed and/or # of cpu's) so I can apply it to other numbers and PCs.

Thanks

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    Oh, you're ignoring the time it takes to read and write data (which is considerable if you've quite the pile of digits)? On computers nowadays, those might take more time than the arithmetic operations themselves...2011-07-16
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    You'll likely be shuttling data in between operations... unless you've big enough RAM, that is. Besides, the architecture of your box is another possible influence...2011-07-16
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    Talking about running time estimation (apart any input/output, memory usage consideration).2011-07-16
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    J.M., what are you talking about??2011-08-15
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    @Tony (didn't get pinged, eh.): He's asking about the time it'll take to factor. My point was that the non-arithmetic operations like moving data around can take more time than the factoring algorithm itself.2011-08-16

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