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2009-03-23, 03:24
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#34 | |
Jun 2005
lehigh.edu
100000000002 Posts |
Quote:
University, of course; as well as the two compute clusters I use for ecm and snfs (and perhaps gnfs, if/when polynomial selection gets more routine above c160). I was using both clusters for ecm, before Greg and Tom's binary and projects (respectively). I'm still spending a lot of cycles on ecm; just not finding factors. Smaller numbers are somewhat more likely to have small prime factors, within ecm range. The Cunningham numbers below C190 have all been tested past t55. Testing past t55 (towards t60) is much harder, with smaller chance of success. Many of these "smallest 100 Cunninghams" may need gnfs; and people doing the sieving will likely be unhappy with factors below p60. Our campus public pcs have condor software installed, which runs from 8pm to 8am. About 1100 cores, c. 400 xps and 700 virtual machines on core2s (two per pc, one on each core, seems to run well, low memory ecm). I ran about a third of the "2nd smallest 100 Cunninghams" from 4*t50 past t55, without finding any factors. Perhaps I'll have better luck if/when I get back to the other two thirds. More generally, many of the Cunninghams in c190-c233 have been tested to 4*t50, except for the ones of difficulty above 250, tested to 3*t50. Likewise, c234-c250 is tested to 2*t50, and c251-c365 to 1.5*t50. On these harder numbers, testing past 2*t50 (towards 4*t50) seemed to give few factors, with the resources I was using at the time, the pcs, plus the x86_64 clusters. Factors were sufficiently sparse that I switched the xps over to BMtR numbers, where ecm was much more productive; on less tested numbers. So anyway, the x86_64 clusters (c. 100 Opterons, 300 cores on dual quadcores) are now doing snfs, when our grad students and other researchers aren't using them for other things. I switch them between projects, NFSNET, C/D, W+D and, most recently B+D (sieving for 2, 1618L has finished). Now that I'm sieving, the pcs are back on Cunningham numbers, but just on near-term sieving candidates. There were some early "successes" with C/D numbers, factors that showed up after polyn and parameters were set, but we ran snfs on the composite cofactors anyway. More recently, 12, 257- gave up a small factor beween 1.5*t50 and 4*t50, leaving a c218. We've had near misses, finding a p60 and a p59 from sieving, on numbers that hadn't been tested that far. Since the pcs aren't being used for sieving, I'm often testing past t55, especially on prospective harder candidates (12, 256+ and 2, 941-, as examples). Lots of ecm curves; just not many factors. Congratulations on the factorization! -Bruce |
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2009-03-26, 00:18
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#35 | |
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Jun 2005
lehigh.edu
40016 Posts |
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As reported above, this number was from c234-c250, which was supposed to have had 2*t50. A cautionary reminder; if one wants p53/p54's removed, that's going to take a bunch more ecm --- that's where the 7*t50's reported on small numbers came from. We'll do better on 5, 362+, the second B+D number, it has the last of 7*t50 running at the moment. -Bruce (not misieve's fault, for sure, the matrix ran right on schedule. See Batalov, elsewhere for details.) |
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2009-03-26, 02:41
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#36 | |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
24·593 Posts |
Quote:
Given the fast progress of the 2LM numbers in page 109, this number emerged from the shadows where it sat for several years (after being ECM'd to 2*t50, probably quite a while ago), so I have no complains that it didn't receive additional ECM cycles. There was no special reason before it jumped into page 110. It goes without saying that generous ECM efforts by Dr.Dodson go to all Cunningham numbers systematically (so if one received just a tad less, some other numbers received more). Those who would have had a heart to complain that 2*t50 was not enough on a number of this size, should first try it themselves; it's a ton of time. And 2*t50 could have found it, but there's always this other chance. So it happened. It was a good test. And there are more factors where it came from.  Serge |
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2009-03-27, 11:11
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#37 | |
Nov 2003
746010 Posts |
Quote:
his web page. |
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2009-03-27, 13:02
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#38 | |
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Jun 2005
lehigh.edu
20008 Posts |
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2009-04-02, 19:45
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#39 | |
Oct 2006
vomit_frame_pointer
36010 Posts |
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On a collection of 60 large composites, ECM'ed already to around t45, 2200 curves at 43e6 found two p45s, a p47, a p48, a p50, p51, a p52, two p53s, and a p54. Of course, that composite which yielded the p52 also had a p47, which I missed. And I missed another couple of p45s, as well as, from what I have seen so far through subsequent sieving, a p47 and a p48, in the same composite, as well as another composite (ECM'ed to 2xt50), with two p51s. I would not be shocked to find that there are 3-4 more p45s hiding in that collection of composites. A year ago I ECM'ed a candidate to t45, found nothing, and pulled a p36 factor by sieving. When I sieve a C199 SNFS and pull a p47, I remind myself that 10^46 is still a large number. BTW, I always enjoy your posts, Bruce. I usually find interesting things in them, and even where I don't understand, I'm engrossed. Last fiddled with by FactorEyes on 2009-04-02 at 19:48 |
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2009-04-03, 18:52
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#40 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
47×229 Posts |
Quote:
 happens.Alternatively, people get very excited when an unusually large ECM factor is found. They get very disappointed when an unusually small one is missed. In reality, both circumstances happen all the time. Paul |
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2009-04-23, 20:04
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#41 |
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Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts |
From my side 6,343+ is 33% sieved so far. Could be relatively faster if the power is more reliable.
Why doesn't someone go on so for 11,229-? It has been standing within the wanted lists for nearly 3 years of time. FactorEyes? No response for that after your last post in Now What (IV) in the factoring forum? Also that, someone could thus take up for 3,509+ after its twin 3,508+ gets completed up... It is too early for me to reserve for my next number... But I am asking so... Is 6,335+ faster by using SNFS or GNFS? In case, it is easy by using GNFS, I don't take it up for my next number... Also that 6,341- even if it is using only a quintic (since it is a multiple of 11), it is rather of difficulty much higher, at 241.23, than 6,343Β± or 6,335Β±? Difficulty = log10(6^310). Otherwise, I rather think of taking the two left over, remaining candidates for my next numbers, thus either 7,393+ or 10,339+ Last fiddled with by Batalov on 2009-04-24 at 01:20 Reason: removed unnecessary quote of the "who" page |
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2009-04-23, 20:10
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#42 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2A0B16 Posts |
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Paul |
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2009-04-23, 20:40
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#43 | ||
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Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts |
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I think that it would be nice if I could see 11,229- and 3,509+ soon. Certainly, it is not a too big project to be done so by fivemack, et. al. in the Factoring Forum, but relatively much easier. Read what I wrote again, to understand what I meant so of. Quote:
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2009-04-23, 21:59
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#44 | |
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Oct 2006
vomit_frame_pointer
23·32·5 Posts |
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