mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2005-04-12, 14:19   #1
wblipp
 
wblipp's Avatar
 
"William"
May 2003
New Haven

23×103 Posts
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.
wblipp is offline   Reply With Quote
Old 2005-04-12, 15:16   #2
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

1001101000112 Posts
Default

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
akruppa is offline   Reply With Quote
Old 2005-04-23, 09:38   #3
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

46438 Posts
Default

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
akruppa is offline   Reply With Quote
Old 2005-04-23, 11:06   #4
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

1D2416 Posts
Default

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.
R.D. Silverman is offline   Reply With Quote
Old 2005-04-23, 11:41   #5
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

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
akruppa is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
A new factor of F11?! siegert81 FermatSearch 2 2018-01-24 04:35
What a (TF) factor!!... lycorn PrimeNet 11 2013-01-12 12:07
New factor for F17 Buckle Factoring 15 2011-03-15 12:05
Bad Factor? nfortino Data 6 2004-12-14 19:25
Shortest time to complete a 2^67 trial factor (no factor) dsouza123 Software 12 2003-08-21 18:38

All times are UTC. The time now is 08:59.


Sat Nov 27 08:59:28 UTC 2021 up 127 days, 3:28, 0 users, load averages: 1.98, 1.27, 1.06

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.