Death
06-14-2004, 09:38 AM
NFSNET clocked up another success yesterday, when this appeared:
Original number had 213 digits:
275761296288173942428817572372378549052834225323290099221816534166117857
14819745
985060521650460193053357181071122907371796448816722717841947241551213691
31414981
87847339287650858740327438890122773007416571133460521
Probable prime factor 1 has 52 digits:
1820248831453728903079155734889112351429153639197869
Probable prime factor 2 has 162 digits:
151496483075854594158209453137387414181447309842040504079843065656803939
53210936
611333719215812770310348024665264342071534533702488449937969713693133849
43700513
09
The 213-digit number is the cofactor of 11^206+1. No primitive factors were known for this number, which was one reason for choosing it. The other reason was that there appeared to be a chance to take the record for the largest penultimate factor.
We missed that one by a very large margin!
It can't really be counted as an ECM-miss, though, because it would have been more expensive (on average) to find the p52 by ECM than it actually was to use SNFS.
More details about the factorization will appear shortly. In the meantime, thanks to all the NFSNET contributors for finishing
another factorization. We have now very nearly caught up with
the backlog caused by M811. The remaining number, 10,223+, should be finished within the week, all being well.
Paul
Original number had 213 digits:
275761296288173942428817572372378549052834225323290099221816534166117857
14819745
985060521650460193053357181071122907371796448816722717841947241551213691
31414981
87847339287650858740327438890122773007416571133460521
Probable prime factor 1 has 52 digits:
1820248831453728903079155734889112351429153639197869
Probable prime factor 2 has 162 digits:
151496483075854594158209453137387414181447309842040504079843065656803939
53210936
611333719215812770310348024665264342071534533702488449937969713693133849
43700513
09
The 213-digit number is the cofactor of 11^206+1. No primitive factors were known for this number, which was one reason for choosing it. The other reason was that there appeared to be a chance to take the record for the largest penultimate factor.
We missed that one by a very large margin!
It can't really be counted as an ECM-miss, though, because it would have been more expensive (on average) to find the p52 by ECM than it actually was to use SNFS.
More details about the factorization will appear shortly. In the meantime, thanks to all the NFSNET contributors for finishing
another factorization. We have now very nearly caught up with
the backlog caused by M811. The remaining number, 10,223+, should be finished within the week, all being well.
Paul