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Old 2005-04-12, 14:19   #1
wblipp
 
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"William"
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Default 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.
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Old 2005-04-12, 15:16   #2
akruppa
 
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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
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Old 2005-04-23, 09:38   #3
akruppa
 
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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
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Old 2005-04-23, 11:06   #4
R.D. Silverman
 
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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.
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Old 2005-04-23, 11:41   #5
akruppa
 
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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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