At 9:12 PM -0700 5/31/08, Kyle Hamilton wrote:
>http://eprint.iacr.org/2007/205 is the most recent I can find.  They
>factored a number of greater than 1024 bits, published on May 31 2007.

They factored a *special* number. The chance that someone would pick 
a Mersenne number as their key is as close to zero as one can get in 
this universe.

As they said in their paper, the effort they used is about the same 
as would be needed for factoring a 700-bit number, and they think 768 
bits is possible for them with a similar hardware setup. The next 
paper from the group should give more detail about the actual 
requirements for the final steps in sieving a non-special 1024 bit 
number.
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