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 2010-06-11, 17:57 #1 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3·419 Posts Extensions to Cunningham tables The extensions to Cunningham 3- tables are available at this website. http://homes.cerias.purdue.edu/~ssw/cun/xtend/index.html 3+ tables as well as other tables will be too extended soon. People can try out with ECM upon these numbers, or also GNFS/SNFS upon those easy candidates. How are the factors being used up? Code: > From raman22feb1988@gmail.com Thu Jun 3 10:20:26 2010 > Subject: How are factors used? > To: Samuel S Wagstaff > > May I know how people make use of that Cunningham factors in other > mathematical works? Where are they used? See Section 2 of my paper http://homes.cerias.purdue.edu/~ssw/cun1.pdf for uses of Cunningham factors. You can search MathSciNet for papers that refer to the Cunningham Book (Brillhart et al.) to see more uses of Cunningham factors. > You told that for extending the tables, you wait for customer requests. > Who are those customers? Some people need the prime factors of 3^n +- 1 (and perhaps other bases, too) to construct elliptic curves with nice properties for cryptography. > How do you drive traffic into your website, how do you make people > visit your site often? If I build up with my own website, then how > can I drive people into my own site, especially that right people? That is a trade secret; I will never tell. > After that 6,355- 6,365- has been done > I hope that 6,349- would be in your next "Most wanted" lists :) > as well as 3,563+ after that 3,562+ has been over, the next hole is > only being at exponent 589 for that base 3 tables actually > What about that for 3,563- 3,569- truncating up with that base 3 tables... No Most Wanted number has been done yet on Page 117. The new Most Wanted list for the next page is likely to be the same as the old one. > Time to extend up with that base 3 tables... > For current limits of that Cunningham tables, base 6,7,8,10 are up to > index 400 while that for base 9 is only actually upto index 300 The Cunningham tables are being extended and you can help. See http://homes.cerias.purdue.edu/~ssw/cun/xtend/index.html > At least those multiples of 3 would be easier beyond 600 index for that > base 3 tables If you respect that Aurifeuillian extension tables for > those numbers splitting up into two parts that are easily being > factorable, then why not respect those splitting up into 3 parts that > are easily factorable, as being two thirds part of that original number > itself? Such as for example > 3,603- 3,621- 3,627- 3,633- 3,651- 3,657- 3,675- 3,681- 3,687- 3,699- > 3,636+ 3,654+ 3,678+ 3,696+ Most of these (all the -) are listed on the page http://homes.cerias.purdue.edu/~ssw/cun/xtend/index.html The others (+) will be added soon. > Sometimes, right now, even multiples of 5, 7, 11, 13 for base 3 tables > extension beyond index 600 are being easily accessible in order to be > factorable, like those of 3,611- I would say that rather this base 3 > tables are indeed strongly lagging behind those of that other tables, > really only actually, right now, by now itself, thus I agree. The 3+ table will be extended soon. > After that, even extension for that base 2 tables will provide provision > in order for others to do work upon that Mersenne Numbers with no known > prime factors list of numbers, that is candidates like > 2,1237- 2,1277- > after that enclosed list of numbers such as those of > 2,1123+ > for which no non-primitive prime factors is being known up so right now, > at all, first of all as well as 2,1061- with no known prime factors at > all, thus indeed really All of the Cunningham tables will be extended, even the base 2 tables. Keep the factors coming! Sam Wagstaff Edit: Yes, of course that I requested for permission in order to share this up from Prof. Sam Wagstaff Last fiddled with by Raman on 2010-06-11 at 18:33
2010-06-11, 18:33   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Raman The extensions to Cunningham 3- tables are available at this website. http://homes.cerias.purdue.edu/~ssw/...end/index.html 3+ tables as well as other tables will be too extended soon. People can try out with ECM upon these numbers, or also GNFS/SNFS upon those easy candidates.
I hope not. What fun is there in doing numbers that are easy?
Let's make more progress on the current tables before extending them.

As soon as the tables are extended, people will go after the low hanging fruit
and ignore the current tables.

 2010-06-11, 18:38 #3 XYYXF     Jan 2005 Minsk, Belarus 24×52 Posts On the other hand, people with smaller CPU power would help on the extended tables, while on the current tables they won't give any help. Last fiddled with by XYYXF on 2010-06-11 at 18:39
 2010-06-11, 18:49 #4 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 145910 Posts And it looks like that sam doesn't use/know the factordb.com, because using that: p=10739917689782934291348634826555020368414408001; is a factor of 3^775-1 found/added by Jonathan Crombie on March 4, 2010, 12:25 am. (by hand I've checked that there is no more factor on this extension table, and added some to the factor database.)
 2010-06-12, 05:20 #5 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 939110 Posts I wonder if anyone (Paul?) knows how much these targets are ECMed. Probably well above 40 digits. I'll do 3,705- for a warmup in one quad-day (diff.180). There's also 3,777- (diff.211), a nice sextic.
2010-06-12, 14:30   #6
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by R.D. Silverman I hope not. What fun is there in doing numbers that are easy? Let's make more progress on the current tables before extending them. As soon as the tables are extended, people will go after the low hanging fruit and ignore the current tables.
Repeated inquiries about the length of the smaller of the 18 tables didn't
get hardly any interest in extending the tables. I wonder whether having
the Smaller-but-Needed numbers headed into the c180's triggered the
extension this time? I can't recall ever having seen the "2nd smallest
available" (& etc, 1st, 3rd ...) listed on the "who's" before, which suggests
that Sam was giving some of his attention to that.

We used to have similar bumps in the available easy numbers back in
the RSA partition Challenge --- factoring the last number in a 10-digit
range would bring a bunch of new numbers up into the range where
points were given (0 points --> 1 points, 1 points ---> 2). Depending
upon how many new numbers are in the pending extension (base-2, even!),
I wonder whether much of the lower low-hanging fruit will have cleared
in a few months, and we can see where things settle. -Bruce

PS -- Maybe we also needed some new Cunningham 2^n-1's for PS3
search targets?

 2010-06-12, 16:09 #7 chris2be8     Sep 2009 2×5×7×29 Posts 3^607-1 is one of the odd perfect roadblocks and has had a lot of ECM run against it, see http://www.mersenneforum.org/showthr...991#post202991 for details. Also 3^661-1, 3^857-1, 3^971-1 and 3^991-1. So don't start running curves shorter than B1=260M against 3^607-1or shorter B1=43M against any of the rest. It would be nice if the tables said how much ECM etc has been run against unfactored numbers to prevent wasted effort. Chris K
2010-06-12, 16:15   #8
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by bdodson Repeated inquiries about the length of the smaller of the 18 tables didn't get hardly any interest in extending the tables. I wonder whether having the Smaller-but-Needed numbers headed into the c180's triggered the extension this time? I can't recall ever having seen the "2nd smallest available" (& etc, 1st, 3rd ...) listed on the "who's" before, which suggests that Sam was giving some of his attention to that. We used to have similar bumps in the available easy numbers back in the RSA partition Challenge --- factoring the last number in a 10-digit range would bring a bunch of new numbers up into the range where points were given (0 points --> 1 points, 1 points ---> 2). Depending upon how many new numbers are in the pending extension (base-2, even!), I wonder whether much of the lower low-hanging fruit will have cleared in a few months, and we can see where things settle. -Bruce PS -- Maybe we also needed some new Cunningham 2^n-1's for PS3 search targets?
Why can't they go after the remaining 2+ and 2LM's???

2010-06-12, 16:53   #9
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

23518 Posts

Quote:
 Originally Posted by R.D. Silverman I hope not. What fun is there in doing numbers that are easy? Let's make more progress on the current tables before extending them. As soon as the tables are extended, people will go after the low hanging fruit and ignore the current tables.
I will be posting up with the extended tables over Mersenne wiki along with current tables in beautiful format shortly, along with sorted difficulty levels separately.

I agree that the extended tables will be a target for people with limited resources as well as a practice tool for newcomers. I think that it is time to expand your world of tables, rather than focusing upon a small room of Cunningham candidates. 3,607- 3,661- have no known non-trivial factors at all.

Let us make use of this thread for extended Cunningham table reservations as well as posting up with new factors? What about that of the extended 3LM tables?

Please explain how factoring up with
$3^{607}-1 \over 2$
help in order to find out new odd perfect numbers (if any does really exist up, in any case), or clear roadblocks or possibilities upto a certain limit.

Last fiddled with by Raman on 2010-06-12 at 16:56

2010-06-12, 17:06   #10
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by Raman I will be posting up with the extended tables over Mersenne wiki along with current tables in beautiful format shortly, along with sorted difficulty levels separately. I agree that the extended tables will be a target for people with limited resources as well as a practice tool for newcomers. I think that it is time to expand your world of tables, rather than focusing upon a small room of Cunningham candidates.
There are over 400 remaining.

Quote:
 Please explain how factoring up with $3^{607}-1 \over 2$ help in order to find out new odd perfect numbers .
It won't. But it can help raise the lower bound.

2010-06-12, 19:13   #11
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

23·113 Posts

Quote:
 Originally Posted by R.D. Silverman Why can't they go after the remaining 2+ and 2LM's???
("They" are presumably are Arjen Lenstra's group at EPFL.) There are several possible answers to this question. The first is that computations modulo 2- are very easy on a binary computer. It's clear that their current software has been written to exploit this.

Another answer is that they haven't (yet) re-coded their arithmetic library to exploit the more difficult but still simple reduction modulo 2+.

A third answer may be that they don't want to. There are still plenty of 2- numbers which have not yet been tested to the p75 level.

You should be able to think of other plausible answers.

Paul

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