The factors of 11,206+.c213 are p52 and p162

[Jeff Gilchrist]

Another number has been factored and here are the results:

NFSNET clocked up another success yesterday, when this appeared:

Original number had 213 digits:
275761296288173942428817572372378549052834225323290099221816534166117857
148197459850605216504601930533571810711229073717964488167227178419472415
512136913141498187847339287650858740327438890122773007416571133460521

Probable prime factor 1 has 52 digits:
1820248831453728903079155734889112351429153639197869

Probable prime factor 2 has 162 digits:
151496483075854594158209453137387414181447309842040504079843065656803939
532109366113337192158127703103480246652643420715345337024884499379697136
931338494370051309


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