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2008-05-30, 23:12
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#144 |
Oct 2006
22·5·13 Posts |
6080<n<7000 is done, with the highest jumping champion at k=129122193. Around 20% done 7000<n<8000
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6895 4761471 6896 5415105 6897 18653271 6898 24237225 6899 25033581 6900 13954353 6901 19993041 6902 33143793 6903 9464829 6904 46026087 6905 30733479 6906 10490763 6907 8663319 6908 1648905 6909 8869395 6910 50639967 6911 11765289 6912 13742025 6913 8265879 6914 358845 6915 15953061 6916 10767633 6917 4156335 6918 15127467 6919 327045 6920 11771535 6921 17417991 6922 2770845 6923 48187065 6924 2057487 6925 349509 6926 52662333 6927 484101 6928 23584317 6929 32493975 6930 30111153 6931 13403661 6932 8206395 6933 17511561 6934 26242197 6935 23812005 6936 8227173 6937 12060831 6938 972303 6939 2458155 6940 16387995 6941 6457779 6942 12704907 6943 34478499 6944 970347 6945 1269285 6946 21349797 6947 26237925 6948 129122193 6949 55222761 6950 5939247 6951 14223135 6952 15309015 6953 3753849 6954 9568125 6955 3616305 6956 430503 6957 14929371 6958 5033685 6959 18471051 6960 8409315 6961 3543321 6962 8878293 6963 23269599 6964 12494697 6965 10486965 6966 5773887 6967 4208451 6968 10338615 6969 433755 6970 2372427 6971 40351479 6972 11679813 6973 2393811 6974 6086847 6975 1023411 6976 12692667 6977 13435509 6978 1657227 6979 3700059 6980 3671745 6981 22638315 6982 1449063 6983 17717769 6984 9992427 6985 4411545 6986 7997367 6987 22550595 6988 3476013 6989 11975079 6990 4794543 6991 35995959 6992 4065555 6993 6961845 6994 7348017 6995 5299875 6996 21651807 6997 7448979 6998 37977237 6999 123585 Last fiddled with by roger on 2008-05-30 at 23:15 |
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2008-05-31, 05:06
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#145 |
Mar 2006
Germany
32×17×19 Posts |
now there's a greater range with new results i will update the first-k-twin-page the next days.
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2008-06-04, 21:52
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#146 |
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Mar 2006
Germany
32×17×19 Posts |
the page with first-twin-k has been updated with new ranges and graphs.
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2008-06-15, 07:49
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#147 |
"Curtis"
Feb 2005
Riverside, CA
486410 Posts |
Following up on Flatlander's idea, or a milder form of it:
If we set NewPGen to include even k's, we can then increment n by 2, right? The even k's from say 50001 would be the candidates from 50002 (unless divisible by 4, in which case they're a duplicate from 50003, or even higher). Is cutting the sieve time in half worth the possible double-testing certain numbers (those divisible by 4, or 16), in an ongoing n-range search? Am I missing some math here that makes this not work? Is there a fairly simple program in DOS or linux to cull the k's divisible by 4? I suppose this is simple to implement, but I have almost-no coding background. I like the ideas in this thread, and have started experimenting with sieves to see how deep things should go. Note that since each n needs its own sieve, the sieve effort is spread throughout the project, instead of upfront; this makes it VERY easy to get ideal sieve depth on a future 450-528,000 twin attack. Each file could sieve to 3 or 4 T in hours, followed by 1000 LLR tests on that file, which is a month or more. It would be painless to stay ahead of an LLRnet server with sieves like that, where the old style of project really needed months of sieving before beginning a search. -Curtis |
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2008-06-15, 13:02
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#148 | |
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I quite division it
"Chris"
Feb 2005
England
31·67 Posts |
Quote:
If you sieve to include even-ns, each even-n will have a unique factorization therefore will simplify to a unique kn pair. The only ones that aren't worth testing are where n is a power of 2, which simplify to Mersenne candidates. ie. Including even-ns make the sieve much more efficient without any filtering out duplicates afterwards. But you won't have to sieve twice as deep. (Is it sqrt(2) as deep??? And how many (%) more candidates are sieved out by the deeper sieving? Anyone?) Also, when LLRing, it will take twice as long to hit the FFT changes/slowdowns. BUT If you then go on to sieve the following ns (or somebody else does), you will get a duplication of effort. This is why I use my technique. To find my reportable twin I tested n from 110,000 to 110,011 in one go, then from 110,012 to 110,023 etc. i.e. No overlapping at all and getting the benefits of a much deeper sieve. IMHO To be honest, I see my technique (or an adaption of it) as ideally suited to a distributed record twin effort. People could reserve, say, 120 n, sieve it themselves and test it themselves. Or we could have presieved files for testing. Sievers would need a program to generate a file for sieving, and a program to simplify the NewPGen output. I have two simple programs that could be adapted/rewritten for general use. Or better still, someone (not me!) could write a program that automatically works with cNewPGen and simplifies and combines the files afterwards, ready for testing. Chris footnote: How many n can be sieved at a time depends on how much memory you want to let NewPGen have, and how high you want to let k go (2^20-1, 2^21-1 etc.) Sieving 10 n at a time, to a k maximum of 4194303 (2^22-1), uses just 64Mb or memory, will produce lots of well-sieved candidates and will keep the FFT size fairly small. If the sieving was always above top-5000 level this would encourage people to participate because Riesels could be submitted. (We would, again, get lots of annoying top-5000 primes but at least they would always be near the bottom.) There would be very little wastage of sieved files if a twin was found. We could just move n up a bit and find another! |
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2008-06-29, 00:09
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#149 |
May 2007
Kansas; USA
242438 Posts |
The "all twin" search for k<1M is now complete to n=48K. 5 twins were found for n=44K-48K as follows:
588207*2^45036-/+1 311541*2^45439-/+1 103893*2^47122-/+1 922713*2^47132-/+1 348429*2^47961-/+1 The web pages have been updated. n=48K-52K is now in progress. All 4 cores of one of my new quads is very quickly catching up to my very slow borrowed siever. Sieving is only around n=53K so it looks like I'm going to have to change it over to a dual-core Athlon within the next week or so. It's taking around 3.5-4 weeks per 4000n on a full quad now, which is too long for my tastes. After n=52K, I'm going to put a 2nd full quad on it to get it up to top-20 range within the next 3-4 months. Gary Last fiddled with by gd_barnes on 2008-06-29 at 00:12 |
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2008-06-29, 02:02
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#150 | |
Jun 2003
22×33×47 Posts |
Quote:
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2008-06-29, 05:13
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#151 | |
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May 2007
Kansas; USA
101×103 Posts |
Quote:
I realize Chris's (Flatlander) method is more efficient for sieving but it requires more manual intervention or would require more programming to automate. Interestingly, it is something I had visualized myself before I ever saw it posted here. It's just that the time-savings isn't great enough from my perspective to make it worth it at the low n-ranges. I may look into it as the CPU-time savings becomes greater at the higher n-ranges. As it is, I just set NewPGen to run and it sieves away a single-n at a time for k=3-1M. After 1000n, I copy all 1000 single-n files into one big 1000n file. I then feed 1 file per core into a quad; 4000n at a time. It's worked pretty well so far. Gary Last fiddled with by gd_barnes on 2008-06-29 at 05:14 |
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2008-06-29, 07:39
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#152 | |
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Jun 2003
22×33×47 Posts |
Quote:
There is a catch. The files themselves will be much bigger than normal after sieving. But once you get rid of the unwanted k's, they'll shrink back to normal. |
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2008-06-29, 16:38
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#153 | |
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May 2007
Kansas; USA
101·103 Posts |
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OK, since within the next 1-2 weeks, I will need to start sieving on a higher-speed machine, I'll give this a shot. Can you send me your script? Thanks! Gary |
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2008-07-01, 02:11
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#154 | |
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I quite division it
"Chris"
Feb 2005
England
207710 Posts |
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