20050216, 13:41  #1 
Apr 2004
Copenhagen, Denmark
2^{2}×29 Posts 
2,709+ factored
Walter Misar has just announced the complete factorization of 2^709+1. Below is a copy of the mail I recieved from Sam Wagstaff:
 Begin mail  The C192 factor of 2,709+ in the wanted list factors as 1829040306801321759939909767617476342912326200121 * 2858393504102843519415883802676938126311662589958254\ 65814552263265276736767979551874964500526866985214814\ 286609216243961894089704553236781434371 I used an ecm implementation following the parameterization given in Brent's paper about the factorization of F10 and F11. The factor was found with sigma=1357251979, a bound B1 of 9,000,000 and a bound B2 of 200*B1. The remaining factor is pseudoprime. Walter  End mail  The group order factors as 2^10 * 3 * 7 * 2099 * 18061 * 23459 * 26903 * 245941 * 1602737 * 7490839 * 1203970723 I was doing this number by SNFS and was 97% done with the matrix, so I guess you can't win every time. The discovered factor is a p49, so I don't know if this factor would have been found on a 45 digit level sweep of the number.  Cheers, Jes Last fiddled with by JHansen on 20050216 at 13:41 
20050216, 14:52  #2 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Nice factor, but shame about the wasted NFS effort!
Doing 5500 curves with B1=11M and gmpecm default parameters would have had a 20% chance of finding this factor. Alex 
20050216, 19:06  #3  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
3×13^{2}×23 Posts 
Quote:
Paul Zimmermann once found a factor of a number that I had started with SNFS, but at least he did so before I'd finished sieving, let alone so close to finishing the factorization. Oh well, better luck next time. Paul 

20050216, 20:40  #4  
"Bob Silverman"
Nov 2003
North of Boston
16524_{8} Posts 
Quote:
OTOH, it illustrates something I have been trying to say: We need more ECM effort on the 2+ and 2 numbers below n = 1200 before we run NFS....... People seem "reluctant" to run ECM on the 2+ tables...... They have not received the same level of effort as other numbers....... BTW, It would be nice to know the actual result....... 

20050216, 20:56  #5  
"Bob Silverman"
Nov 2003
North of Boston
16524_{8} Posts 
Quote:
Notices had gone out (and the GIMPS projected indicated) that 2,709+ was 'reserved'. While I applaud friendly competition, it would be nice NOT to waste time by duplicating efforts. Is it unreasonable of me to request that people stop ECM efforts on a number when someone else indicates that they are doing it by NFS? I am hoping to get access to some resources that will let me do 2,1294L, 2,719+, 2,737+ and 2,749+. Perhaps people might attack these numbers with ECM to the 50 digit level *before* I make the effort? 

20050217, 09:01  #6 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
2,719+, 2,737+, 2,749+ all fit in a length 32 DWT (threshold 753), so stage 1 for these can be done very efficiently on Pentium 3 cpus with Prime95 v23.
I'll start with 1000 curves at B1=44M on 2,719+. Alex 
20050217, 12:55  #7 
Mar 2003
New Zealand
13·89 Posts 
I have been working on 2,719+, 2,736+ and 2,751+ and have done about 1000 curves (B1=44e6, B2=1000B1) on each so far, I will probably do about 1000 more. Is it worth working on 2,737+ or 2,749+ any further? I thought these were easier with NFS now.

20050217, 13:31  #8  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
in my opinion before I do them with NFS. Please remember to report your trials to George Woltman 

20050217, 13:43  #9  
Mar 2003
New Zealand
13·89 Posts 
Quote:


20050226, 06:29  #10 
Jan 2005
2×31 Posts 
Is there a list of 'reserved' Cunningham numbers available?
Does anyone keep a master list of currently reserved numbers? As of today (25 Feb 05) I'm aware of the following:
Paul Zimmerman's c120355 table (http://www.loria.fr/~zimmerma/records/c120355) lists seven numbers reserved 12,297 C190 Montgomery 7, 511L C167 Dodson 2, 963 C185 Dodson/Lenstra 12,242+ C209 Montgomery 12,218+ C191 Montgomery 2, 739 C168 Franke 2,1173 C146 Kleinjung In addition, the NFSNET site (http://www.nfsnet.org/) indicates that sieving is complete for 5, 307+ and started on 7, 254+. Anyone know of other sources? 
20050226, 08:03  #11 
Apr 2004
Copenhagen, Denmark
2^{2}·29 Posts 
The Cunningham wanted page: http://www.cerias.purdue.edu/homes/ssw/cun/want95 also lists a few reserved numbers.
I'm currently working on 3,436+, and then I plan to do 3,437+. As a little side project I'm also factoring 11,236+.C136 using Chris Monico's ggnfs together with Tom Cage.  Cheers, Jes 
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