20050412, 14:19  #1 
"William"
May 2003
New Haven
924_{16} 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 notyetreadyforprimetime Search for Odd Perfect Numbers.

20050412, 15:16  #2 
"Nancy"
Aug 2002
Alexandria
2^{5}·7·11 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 
20050423, 09:38  #3 
"Nancy"
Aug 2002
Alexandria
2^{5}·7·11 Posts 
Pascal did it again, this time a p57 of the c133 of 3719^371. 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 
20050423, 11:06  #4  
Nov 2003
2^{6}×113 Posts 
Quote:
This number would be much better done with GNFS. 

20050423, 11:41  #5 
"Nancy"
Aug 2002
Alexandria
2^{5}×7×11 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 20050423 at 11:46 Reason: post scriptum 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A new factor of F11?!  siegert81  FermatSearch  2  20180124 04:35 
What a (TF) factor!!...  lycorn  PrimeNet  11  20130112 12:07 
New factor for F17  Buckle  Factoring  15  20110315 12:05 
Bad Factor?  nfortino  Data  6  20041214 19:25 
Shortest time to complete a 2^67 trial factor (no factor)  dsouza123  Software  12  20030821 18:38 