20220826, 15:37  #1 
May 2003
3·5·17 Posts 
Can I borrow some ECM of a friendly CPU?
Working on something a bit cranky at the moment, where the act of discovery is the main pleasure, hence my secrecy, I'd rather not be spoiled  I'll post here more about it when I've run out of easy ideas, but in order to progress down one of my branches it would be nice if I could get some prime factors from a big number or two...
I've done an hour or so of gmpecm on my very ancient celeron (I'm trying to go fanless at home, so have no number crunchers any more), but if someone could run on a punchier box for a few hours, I'd be grateful. The larger the prime factors, the less useful it's likely to be, so there's no desperate need to squeeze until the blood comes out. Code:
2232027714105126816428496408520838343541574716773833234422858719802554161115433284979455602363125877584353560031892174122433028819199338161851711418563679155788334827984879707802194586760032236380533301339398039260132519982610980345662291040085036304200947886685065197112458200057264014024939561484682779714092311963567553241820332104244058889838075512885630103419457958234260809678171117972292268560997359961117264021124933193154972706036460580485672015007550644880805972874512654905555137943723971508484120141668255734453799834345615461799656754596993464424308713463364302328004514033836254716138875402216038222489970056543392748779302754044583602086957893207732343610979066203896281666364562222744443062516699025933511360276131202422714654083269505722655540186872282583773385792650167573211756010416352186314712976030741409505933682844296361336030384873190748192334103858433474918930981694692115809670053438860819719522519400485727410389010472402762612125130999773017467969736471680501015206419372158919496944457986473959477 Last fiddled with by frmky on 20220826 at 18:42 Reason: Put large number in a code block 
20220826, 17:06  #3 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×3,557 Posts 
Alpertron's page finds the tiny factors 3 ร 7^{4} ร 23 in a flash. Maybe you have an NVIDIA GPU suitable for GPU assisted ECM? https://download.mersenne.ca/GMPECM
(And I'm wondering why post one text does not line wrap, like other posts do, but require lateral scrolling. Guessing it's the unformatted 1027digit number.) Last fiddled with by kriesel on 20220826 at 17:13 
20220826, 18:28  #4 
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{4}×7×11 Posts 
On the cofactor, I am running t35 and P1 with B1=200000000, B2=12721007621976 (automatic B2).

20220826, 23:46  #5  
"Robert Gerbicz"
Oct 2005
Hungary
7×229 Posts 
Quote:


20220827, 08:15  #6  
May 2003
3·5·17 Posts 
Quote:
As I make progress, it looks like I only need 1 factor per term, and that was already a cofactor, so I think I don't need any others from (the nonmangled version of) that one at the moment. Annoyingly, the terms double or treble in size with each step, eventually it will become quite a trudge. gmpecm is amazing though, you only really appreciate how good things are when you depend on them! I'm not sure I understand the OEIS series posted, but there is a very strong sqrt(5) connection, which makes the fib link quite interesting. Fortunately, the sequence I'm working on has a companion sequence, and I will attack that with the most logical approach that I've perversely evolved whilst attacking the first one, so I can put together a more coherent webpage on what I'm doing. Still continuing, fraction by fraction... Last fiddled with by fatphil on 20220827 at 08:30 

20220827, 12:54  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{6}·181 Posts 
Quote:
You should still have my nonMSFT email address (PM if not) so send me the number and I will see what I can do. Paul 

20220828, 12:39  #8  
May 2003
3·5·17 Posts 
Quote:
I've pushed forward as far as I can, and have finally hit a number I can't get anything from at all. I'm up to a 80kdigit composite now. Did 100 curves from B1=10k22k overnight, and pushing forward with 100 more from 22k50k now. I've stuck the number in a text file here: http://ircing.org/~fatphil/composites.txt (Note to internet citizens of the future, that URL won't last, I'm temporarily borrowing a friend's big box to do the ECM work.) Fortunately, I don't actually *need* to know any factors, this is mostly just trying to optimise the size of what I was searching for  a covering set. There's no shame in throwing a composite in such a set, if it covers, it covers, it's just a neatness thing. It's unsatisfying to not even know one prime at its apparition time. There are two parts to this hunt, and part 1 had a perfectly neat pattern of removing half the candidates with each factor found. Part 2 has a perfectly neat pattern of absolutely no pattern appearing at all. I presume that part 1 has some algebraic structure, which might imply that my hunt will never terminate, I'll just chop the integers in two forever, and my conjecture is unprovable. I'll put together an HTML page today or tomorrow explaining the whole thing, so some proper mathematical minds can shed some light on the matter. Alas I've got tens of megabytes of Pari/GP output that I need to filter through. It's all a bit of a mess currently. I've been in scatterbrained scientist mode! 

20220828, 14:40  #9  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{6}×181 Posts 
Quote:
Have you run P+1 and/or P1 and, if so, how far? P1 with B1=10K, B2= 632208 took 27s and 2214s I didn't expect to find a factor, just calibrating this machine. 

20220828, 15:49  #10  
May 2003
11111111_{2} Posts 
Quote:
Run 25 out of 100: Using B1=25937, B2=259376825010, polynomial x^1, sigma=0:13064782877481766227 Step 1 took 890799ms Step 2 took 167704ms Anyway, the first 10 minutes of investigation, which got me caught in this rut, is now presented here (I'll try to pull the relevant steps forward out of my GP history tomorrow, no more time today): http://fatphil.org/maths/sqrt_cf/sqrt5.html 

20220828, 17:07  #11  
May 2003
377_{8} Posts 
Quote:
But tonight is sauna night, so I'm happily tucked away there for the rest of the evening. Last fiddled with by fatphil on 20220828 at 17:07 

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