I agree too. We should be realistic. That team that factored the 768 bit number took two years to do it. If they factored a 1024 bit number with the same resources, it would take about as long as factoring 2^256 of those 768 bit numbers.

My cores are usually working on stuff more useful than TF'ing 1024-bit numbers
That I know fully well that TF'ing 1024-bit numbers is impractical (I was the second person to write it in the topic, an hour after bwang ) does not mean that I cannot help speeding up the program (as a ways to learn a bit about the GMP API, which I had never used before) and make my computers spend a reasonable amount of time trying. I might end up unfathomably lucky, after all - and if not, no biggie, I knew it was impractical

What is the "only practical method"? I thought the GNFS was currently the fastest algorithm for factoring large integers with no special form.

Yes, it is GNFS. But we don't have access to the special implementation of GNFS + post-processing steps that enabled factoring RSA-768, made by the top researchers in the field
And anyway, even if we had it, I don't think it would be that useful to us, as some pieces of it would probably need some improvements so that they can scale up three orders of magnitude in difficulty, for factoring RSA-1024. Only the top researchers of the field can make the (probably) needed improvements.

See reply #70, http://ourl.ca/6236/101082

hey, on a side note, think of how famous the ti-community would be if we factored ANY 2048 bit key, not specifically the nspire's. so, ponder this: if you multiply two 2048 bit keys together, and try to factor that, you now have to locate one of 4 possible prime numbers in a field that is no larger than if you were factoring a single key alone. you've just doubled your chances, which halves the amount of time it takes to do it! with 4 keys together, you could factor one of them in 1/4 the time!!!! actually, its a little longer than that because you're working with a bigger number, but still!!!! ok, so we won't be able to factor the specific key we want, necessarily, but we'll still be famous for being the first people to factor a 2048 bit RSA key!!!

oops, sorry! I meant to say 1024 bit. I was just testing you all....slash, I was 50 years ahead in computer technology. good job DJ!

hey, on a side note, think of how famous the ti-community would be if we factored ANY 2048 bit key, not specifically the nspire's. so, ponder this: if you multiply two 2048 bit keys together, and try to factor that, you now have to locate one of 4 possible prime numbers in a field that is no larger than if you were factoring a single key alone. you've just doubled your chances, which halves the amount of time it takes to do it! with 4 keys together, you could factor one of them in 1/4 the time!!!! actually, its a little longer than that because you're working with a bigger number, but still!!!! ok, so we won't be able to factor the specific key we want, necessarily, but we'll still be famous for being the first people to factor a 2048 bit RSA key!!!

I think the community would become famous if we did just crack the 1024 bit key.  Has this ever been done before?  The community even got some publicity with the 512 bit keys!

I think you were thinking add, or multiply by two.

no, i actually meant multiply the 'n' values for two different keys together. the resulting number has 4 primes, each having about half as many digits as ONE of the n's. the probability of selecting a correct factor is doubled.

One team actually did crack a 1024-bit key, but it wasn't through a factoring method. It was by starving the cpu of electricity, giving out tiny parts of the factor along with a bunch of other stuff. It took 11 months, and isn't applicable to the nspire, because of how it's factored.

Check out the article here
http://www.engadget.com/2010/03/09/1024-bit-rsa-encryption-cracked-by-carefully-starving-cpu-of-ele/