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Old 2003-01-18, 13:42   #1
jocelynl
 
Sep 2002

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Default Factor found on M809

Hi George,

I noticed that a factor was found on M809. Do you know who found it and what method as been used?
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Old 2003-01-18, 14:15   #2
smh
 
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From the ECMNET page (the c120-355 page):
[list] 244 2, 809- 3414023389634485388328884116849283992138116261025744978122883999623187065762627620618973286846235796//
244 ........... 8603801142238378191082950664469091149211460382987933849836007206807111754539330960823868487806612300//
244 ........... 88261573940214625662995187948181075905216511
t35 Curry + 19204*44e6 Franke t50
done 4148386731260605647525186547488842396461625774241327567978137 Franke et al. 03.01.03 SNFS
removed[/list:u]
Is this a record size SNFS factorization?
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Old 2003-01-18, 15:14   #3
Prime95
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Sieving was done at the CWI, at the Scientific Computing Institute and the
Pure Mathematics Department at Bonn University, and using private resources
of J. Franke, T. Kleinjung and the family of F. Bahr. The linear algebra step
was done by P. Montgomery at SARA in Amsterdam. Postprocessing (other than
the block Lanczos step) was done in Bonn


I do not know if this is a record SNFS factorization.
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Old 2003-01-18, 17:46   #4
cperciva
 
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Richard Brent (who happens to be my DPhil supervisor) says that he thinks this is the current SNFS record.
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Old 2003-01-18, 20:18   #5
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As far as i know, the old record was 2^773 + 1 (233 digits)

ftp://ftp.cwi.nl/pub/herman/SNFSrecords/SNFS-233
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Old 2003-01-20, 12:55   #6
nuutti
 
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Default Records site

I think that here is a kind of record list :
http://www.cerias.purdue.edu/homes/ssw/cun/champ


Yours,

Nuutti
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Old 2003-01-21, 18:16   #7
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Thanks to Jocelyn and Sander for raising the question and finding the answer. I had been curious about M809 and had been hoping for some kind of announcement from the factorers. 244 digits - wow! Unfortunately, the smaller factor was "almost" in reach of ECM. I had been hoping for a new penultimate factor record, which is currently the 98-digit factor of M727 found by Dodson/AKL/CWI, but sooner or later, this record will fall, too!
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Old 2003-01-21, 19:11   #8
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If you call 61 digits "almost" then you're right ;)

I had seen the page nuutti gave before, just couldn't find it straight away.
[list]Special number field sieve by SNFS difficulty:
4703 C227 2,751- CWI/Dodson/Franke/AKL/Leyland
4530 C227 2,773+ The Cabal[/list:u]

Just wondering, why has 2,751- a higher SNFS difficulty? 2,773+ seems larger.
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Old 2003-02-03, 01:30   #9
philmoore
 
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Default Another one

Here's another one, the completed factorization of M719, from the same page cited by smh above:

208 2, 719- 2481831853628975239734324283683350274917109400971062161087619357919015825532905467342080904365328434$
208 4339425991997685971628441277106032413489516858866309585344149133273061723293256127420536552444883737$
208 54631919
1870*1e6 (C. Curry) + 5040*3e6 (Curry) + 2051*11e6 (Curry) t40
done 737572843389436536903316910033561929012829990389769 Dodson/AKL/CWI/Leyland SNFS 07.01.03

This 51-digit factor probably could have been found more easily with about one year's worth of ECM on a fast P4 or Athlon. My guess is that the factorers found M719 a tempting target because the unfactored part, at 208 digits, seemed to offer a possibility of breaking the 98-digit penultimate factor record.

I see that the NFSNet project: http://www.nfsnet.org/
has started work on M673, the smallest Mersenne number not yet completely factored. The next two Mersenne numbers on the list, M713 and M731, have had considerably less ECM effort than M673, probably because the exponents are composite. (713=23*31 and 731=17*43.) Is anyone feeling lucky? Finding a factor of either of these could save the SNFS folks a lot of work down the road! See:
http://www.mersenne.org/ecmm.htm
for ECM status.
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Old 2003-02-27, 20:37   #10
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So, which number should we do first, M713 or M739, where 739 is prime? I can put three P4's to work for one or two weeks.

Note: M739 was affected by the bug in version 22.12 and earlier, and I ran 5000 curves up to B1=11000000. Now I've just rerun them, with the corrected version, but I didn't find any factor :( .
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Old 2003-02-27, 21:31   #11
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I'd say all three numbers, M713, M731, and M739 look like good candidates. You could put each P4 to work on a different candidate! M713 has a C171 cofactor, M731 has a C183 cofactor, and M739 has a C168 cofactor. I've already run about 300 curves on M713 with B1=44000000 on an old 233 MHz Pentium! My guess is that we don't always know how much work has been done by the ECMNET group, and that at B1=44000000, there is a reasonable chance that a record ECM factor of > 55 digits just possibly could show up.

Sorry to hear that your M739 curves were affected by the bug. That bug was an unusual one, affecting exponents near FFT boundaries.

Good luck!
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