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Old 2005-02-16, 13:41   #1
JHansen
 
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Default 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 2005-02-16 at 13:41
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Old 2005-02-16, 14:52   #2
akruppa
 
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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
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Old 2005-02-16, 19:06   #3
xilman
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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
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Old 2005-02-16, 20:40   #4
R.D. Silverman
 
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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.......
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Old 2005-02-16, 20:56   #5
R.D. Silverman
 
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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?
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Old 2005-02-17, 09:01   #6
akruppa
 
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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
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Old 2005-02-17, 12:55   #7
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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.
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Old 2005-02-17, 13:31   #8
R.D. Silverman
 
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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
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Old 2005-02-17, 13:43   #9
geoff
 
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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.
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Old 2005-02-26, 06:29   #10
PBMcL
 
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Default 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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Old 2005-02-26, 08:03   #11
JHansen
 
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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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