To clarify, this is not a new factoring record for products of two primes. RSA-768, a 232-digit number (22 digits longer) was factored in 2009, and that record still stands. <a href="http://en.wikipedia.org/wiki/RSA_numbers#RSA-768" rel="nofollow">http://en.wikipedia.org/wiki/RSA_numbers#RSA-768</a><p>The algorithm used here is GNFS (general number field sieve), which is the same algorithm that's been used for about two decades. In other words, this has no impact on the security of RSA.<p>More information: <a href="http://en.wikipedia.org/wiki/Integer_factorization_records" rel="nofollow">http://en.wikipedia.org/wiki/Integer_factorization_records</a>
"RSA-210" is the official name for this challenge, but it is a bit of a misnomer. The modulus has 210 <i>decimal</i> digits but about 210 * log2(10) = 697 bits.<p>EDIT: Wikipedia article says 696 bits.
In case you've never heard of the challenge: <a href="https://en.wikipedia.org/wiki/RSA_Factoring_Challenge" rel="nofollow">https://en.wikipedia.org/wiki/RSA_Factoring_Challenge</a>
From the logs:<p><i>> Mon Sep 23 11:09:41 2013 commencing Lanczos iteration (32 threads)</i><p><i>> Mon Sep 23 11:09:41 2013 memory use: 26956.9 MB</i><p><i>> [...]</i><p><i>> Thu Sep 26 07:17:57 2013 elapsed time 51:56:44</i><p>I’m not sure that I’m understanding all the details. Does this mean that they factored a 210-digit number in 52 hours in a single machine?
I was curious as to how the cash prizes [1] for this challenge compared to playing the lottery. Consider the next smallest one left: RSA-768. By my very rough estimates [2], $1 worth of computing time on a typical desktop gives you a probability of 10^-58 of factoring the prime by picking random numbers smaller than its square root.<p>[1] <a href="https://en.wikipedia.org/wiki/RSA_Factoring_Challenge" rel="nofollow">https://en.wikipedia.org/wiki/RSA_Factoring_Challenge</a>
[2] <a href="https://www.google.com/#q=%241+%2F+(%240.09+%2F+kwh)+%2F+100+watt+*+100e9%2Fsecond+%2Fsqrt(4120234369866595438555313653325759481798116998443279828454556264338764455652484261980988704231618418792614202471888694925609317763750334211309823974)" rel="nofollow">https://www.google.com/#q=%241+%2F+(%240.09+%2F+kwh)+%2F+100...</a>
What hardware is used for the first round of sieving? Is it "just" distributed computing on normal machines, or are they using special FPGA farms?