mersenneforum.org P56 ECM Factor
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 2005-04-12, 14:19 #1 wblipp     "William" May 2003 New Haven 44718 Posts P56 ECM Factor Today Pascal Ochem reported a 56 digit ECM factor. Paul Zimmermann's Top 100 List has it as the seventh largest ECM factor ever found. Pascal has been working from the Composites Page of the not-yet-ready-for-prime-time Search for Odd Perfect Numbers.
 2005-04-12, 15:16 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts It was one of the weird cases where ECM found the larger prime factor. The input number was only a c103, the cofactor is a p48. While this is a very nice factor, it will probably not be counted on Richard Brent's record factors list - MPQS would have been a much better choice for this number than ECM with such high bounds. Alex
 2005-04-23, 09:38 #3 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Pascal did it again, this time a p57 of the c133 of 3719^37-1. This time he found the smaller prime factor, and it seems it will just barely make Brent's Top Ten list. The condition is 2. Let r = length of input (composite) / length of factor (prime), where the lengths are measured in decimal digits. To be included a factor must satisfy r >= 2.2. [...] Now 133/57=2.33, so the factor should make the list, even though the ratio log(c133)/log(p57) = 2.1. Alex
2005-04-23, 11:06   #4
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by akruppa Pascal did it again, this time a p57 of the c133 of 3719^37-1. This time he found the smaller prime factor, and it seems it will just barely make Brent's Top Ten list. The condition is 2. Let r = length of input (composite) / length of factor (prime), where the lengths are measured in decimal digits. To be included a factor must satisfy r >= 2.2. [...] Now 133/57=2.33, so the factor should make the list, even though the ratio log(c133)/log(p57) = 2.1. Alex
Actually, there are several tiny factors (5/6 digits) that bring it down to C119.
This number would be much better done with GNFS.

 2005-04-23, 11:41 #5 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Oh, correct! I was looking at the SNFS difficulty column in the table on William's page, not the cofactor size column. So again no entry in Brent's table. Alex PS: actually, at SNFS difficulty only 133, this would still have been a SNFS job. Last fiddled with by akruppa on 2005-04-23 at 11:46 Reason: post scriptum

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