mersenneforum.org Gratuitous factors thread
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 2008-02-27, 05:22 #2 jasong     "Jason Goatcher" Mar 2005 66618 Posts I've never tried any of these programs, except ecm. When you talk about failures, is it stuff that you have to tweak, or does the program have some sort of method for cycling through various combinations? I have no idea what kind of combinations, but it seems like there are different variations that can be tried, or maybe I'm just reading non math intensive comments in the factoring threads wrong. (It's fun to scan the math threads for stuff that makes sense. Not that the rest is nonsensical, but if you don't have the knowledge it's mostly gobble-de-gook. :) )
2008-02-27, 12:15   #3
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by fivemack The final factorisation of a C185 as a product of two P93s was a fairly easy SNFS job which happened to have a pretty result: I reckoned that Fibonacci numbers should have the same sorts of identities as Cunningham numbers do, and so used pari's linear-dependency code to find relations between fib(1057)/fib(151) and the terms a^6, a^5b, a^4b^2, a^3b^3, a^2b^4, ab^5, b^6 for a and b Fibonacci numbers.
Sorry to post off-topic, but what is meant by something like "C185" or "P93"?
Just as I'm asking this question I thought of what it might be, just based on the letters...C185 means a composite, 185-digit number, and P93 means a prime, 93 digit number. Is that shot in the dark at all right? Or something to do with Cunningham numbers?

Yes, that's correct -- fivemack

Last fiddled with by fivemack on 2008-02-27 at 13:16 Reason: answered in place

 2008-03-05, 15:28 #4 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 6,323 Posts Lucas(1233) = Code: 19 * 45702379 * Lucas(411) * 44287282091880235117923432515961253359268605892636945776483995749 * 159539728465877952283323572019287689118580024745329748535563445093460821051903111798130855082136071 SNFS difficulty 171.8, took about a week on a few computers, would have been quicker if the reaction to running out of disc quota on the server wasn't to lose writes silently so one file had 200MB of zeroes in the middle where relations should have been.
2008-03-05, 16:06   #5
R.D. Silverman

Nov 2003

26·113 Posts

Quote:
 Originally Posted by fivemack reaction to running out of disc quota on the server wasn't to lose writes silently so one file had 200MB of zeroes in the middle where relations should have been.

Welcome to the club!!!!!

I've had entire collections of sievers shut down because some retard
decided to dump multi-gigabytes of data onto a shared file system and
thereby run it out of space. It leaves corrupted records at the ends
of my output files. This has happened at least a half-dozen times.
Naturally the users who do this never bother to check if there is enough
space before they dump their data......

2008-03-07, 02:46   #6
maxal

Feb 2005

25210 Posts

Quote:
 Originally Posted by fivemack I reckoned that Fibonacci numbers should have the same sorts of identities as Cunningham numbers do, and so used pari's linear-dependency code to find relations between fib(1057)/fib(151) and the terms a^6, a^5b, a^4b^2, a^3b^3, a^2b^4, ab^5, b^6 for a and b Fibonacci numbers.
I think this is a variant of formula (47) at http://mathworld.wolfram.com/FibonacciNumber.html for k=7 and n=151.
This formula can be used directly to get a polynomial representation of degree k-1:

$F_{kn}/F_n = \sum_{j=1}^k {k\choose j} F_j x^{j-1} y^{k-j}$

where $x=F_n$ and $y=F_{n-1}$.

2008-03-09, 16:34   #7
bsquared

"Ben"
Feb 2007

64158 Posts

Quote:
 Originally Posted by fivemack There are enough post-primes-here threads around the forum; why not have a straight factor-reporting thread?
I like this idea. I respect what the prime finding people are doing, but for whatever reason I like factoring instead. So I'll post the biggest factorizations I've done by various methods, and post updates as I break my own records. I think that is the spirit of this thread, no?

Most of these efforts come from the odd perfect number search (http://www.oddperfect.org/), which I've been involved with for a year or so now.

To start:

421^59-1 (C144, difficulty 157.46) by SNFS factors as
8769524964618840768473228417817739675245059818515901 *
35824627104830457305942978653803062873922140670229459114188957954764951096171385903989548363

using the polynomial
c5: 1
c0: -421
Y1: -1
Y0: 31001674351559225686692396607441

6M relations from ggnfs 13e siever on one core of a Athlon64 2.2GHz for a few days followed by msieve postprocessing to produce a 395010 x 395258 matrix with weight 25331768

- ben.

 2008-03-09, 16:43 #8 bsquared     "Ben" Feb 2007 13·257 Posts By GNFS, the 125 digit cofactor of 1119387697^19-1 factors as 3484602912243398707185898705317541418197499305758241 * 8829353630392603956189074833285818490567582542294628525126057810179844037 ~10M relations over a week or so of sieving on one core of a 2.2GHz Athlon64, followed by msieve postprocessing to produce and solve a 826086 x 826334 matrix with weight 60653808.
 2008-03-09, 16:52 #9 bsquared     "Ben" Feb 2007 13·257 Posts By P-1, the C135 cofactor of 64271^37-1 factors as 274817637397314759415229527351079 * P102 using a version of P-1 which I wrote, with a stage one bound of 1e8 and stage two bound of 2e9.
 2008-03-09, 16:59 #10 bsquared     "Ben" Feb 2007 13×257 Posts By QS, 11^174+10^174 (C103) factors as 8055091904195531129734494480052194800703416701 * 282676276623675825398802382490193608881327644834991216513 after about 5 hours sieving using msieve 1.33 on 4 Xeon 5160 cores
 2008-03-17, 23:08 #11 joral     Mar 2008 5·11 Posts A couple of SNFS results I've just completed a few factorizations from the homogeneous cunningham reservation list. Code: 11,6,136+ (C134) 917147464621732445846263197551265176491969916515669969.P80 11,8,136+ (C116) 3019860452197352866441914806309105477611721850147079815601.P59 11,9,136+ (C119) 20392009066511518061382980231029180353909229649.P73

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