2,709+ factored

JHansen · 2005-02-16, 13:41

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

akruppa · 2005-02-16, 14:52

Nice factor, but shame about the wasted NFS effort!

Doing 5500 curves with B1=11M and gmp-ecm default parameters would have had a 20% chance of finding this factor.

Alex

xilman · 2005-02-16, 19:06

Quote:

Originally Posted by JHansen

Walter Misar has just announced the complete factorization of 2^709+1.

...

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.

It's really sickening when that happens. My commiserations.

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

R.D. Silverman · 2005-02-16, 20:40

Quote:

Originally Posted by xilman

It's really sickening when that happens. My commiserations.

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

I know how he feels. It has happened to me.

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.......

R.D. Silverman · 2005-02-16, 20:56

Quote:

Originally Posted by R.D. Silverman

I know how he feels. It has happened to me.

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.......

A follow-on note:

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?

akruppa · 2005-02-17, 09:01

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

geoff · 2005-02-17, 12:55

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.

R.D. Silverman · 2005-02-17, 13:31

Quote:

Originally Posted by geoff

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.

They are easier than (say) 2^736+1 but finishing them to 45 digits is worthwhile
in my opinion before I do them with NFS.

Please remember to report your trials to George Woltman

geoff · 2005-02-17, 13:43

Quote:

Originally Posted by R.D. Silverman

They are easier than (say) 2^736+1 but finishing them to 45 digits is worthwhile in my opinion before I do them with NFS.

The 45 digit levels for 2,737+ and 2,749+ were finished a few months ago by akruppa, Mystwalker and myself. The effort is recorded in the current tables.

PBMcL · 2005-02-26, 06:29

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 c120-355 table
(http://www.loria.fr/~zimmerma/records/c120-355)
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?

JHansen · 2005-02-26, 08:03

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

2005-02-16, 13:41	#1
JHansen Apr 2004 Copenhagen, Denmark 2²×29 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 200B1. 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 2005-02-16 at 13:41

2005-02-26, 06:29	#10
PBMcL 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 c120-355 table (http://www.loria.fr/~zimmerma/records/c120-355) 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?

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2005-02-16, 14:52	#2
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Nice factor, but shame about the wasted NFS effort! Doing 5500 curves with B1=11M and gmp-ecm default parameters would have had a 20% chance of finding this factor. Alex

2005-02-17, 09:01	#6
akruppa "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

2005-02-17, 12:55	#7
geoff 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.

2005-02-26, 08:03	#11
JHansen Apr 2004 Copenhagen, Denmark 2²·29 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