A Mighty Number Falls

space_in_your_face writes "An international team has broken a long-standing record in an impressive feat of calculation. On March 6, computer clusters from three institutions (the EPFL, the University of Bonn, and NTT in Japan) reached the end of eleven months of strenuous calculation, churning out the prime factors of a well-known, hard-to-factor number — 2^1039 - 1 — that is 307 digits long." The lead researcher believes "the writing is on the wall" for 1024-bit encryption. "Last time, it took nine years for us to generalize from a special to a non-special hard-to factor number (155 digits). I won't make predictions, but let's just say it might be a good idea to stay tuned."

Comments

Re:What are they?

[Michael Woodhams]

This is incorrect.

The two factors are prime, and multiply to the given number, but that number is not 2^1039-1.

2^1039-1=
58906808643168367664473872491774762471193869645981 5017753575689937658432079465\
55599325913849006501403400638916156258175437632231 4451080388584562460719428810\
76106983317459922215338711318936320121062386221739 2146903328852155899782370013\
71848062018269073686695341125238207265913549121033 4387684495620912657652829388\
7

And the winning number is...

[SharpFang]

So...
0x7fffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffe
is prime...
Interesting :)

Who's first to write it as decimal here?
Who's to beat the lameness filter while writing it in binary?