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RE: [PrimeNumbers] Re: How fast is a brute force prime gap hunt?

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  • Nuutti Kuosa
    When selecting how high to sieve I have tried to balance these numbers (from my earlier posting) : ... I have calculated ratio 109872444 values left / 4598117
    Message 1 of 5 , Nov 1 2:31 PM
      When selecting how high to sieve I have tried to balance
      these numbers (from my earlier posting) :
      sieve :
      > ** There were 3563266 values removed in the last minute or so

      and gapper:
      >File nude loaded. 109872444 values left, sieved to: 752500739
      > Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
      > 4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]

      I have calculated ratio 109872444 values left / 4598117 prp chks = 23,90
      and multipled prps/s and this ratio = 23,90 * 4053 =96868 effective prps / s
      = 5,812,080 effective prps /min

      so I sieved little too high (may be one minute). But right sieving amount
      depends on size of memory.

      Yours,

      Nuutti


      -----Original Message-----
      From: jfoug@... [mailto:jfoug@...]
      Sent: 1. marraskuuta 2001 23:23
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Re: How fast is a brute force prime gap hunt?


      --- In primenumbers@y..., "Nuutti Kuosa" <nuutti.kuosa@i...> wrote:
      > It depends on number size. :-)

      It also depends heavily on the memory in the PC. More memory, and
      CPAPSieve will process larger ranges, and you can possibly push the
      sieve a little higher (10-100x), thus gapper will have to check
      fewer numbers on average to find prp's. It certainly takes some
      "fine tuning" to determine what the best sized range to work with, and
      what the best level is to sieve to, to minimize the time taken to
      process a range. You are currently running at 510 to 520 seconds per
      billion range (as listed 4 billion in 34 minutes)

      > number 2^116 + k, k from 1 to 4,000,000,000
      > sieving up to 752,500,739 took 15 min, using my P450
      > From sieving program :
      >
      > ** There were 3563266 values removed in the last minute or so
      > 22:04:56: 109887354 ski's left.. 750414773 is a factor of
      2^116+2496270853
      > 22:04:56: 109872444 k's left..
      > sieved up to prime 752500739.
      >
      > File nude saved. 109872444 values stored
      >
      > Then gapper :
      >
      > --klip --- klip --
      >
      > D:\matikka\primegaps\speedtest>gapper -g=2000 nude
      >
      > +-------------------------------------------------------------------
      +
      > | Gapper v1.30 Finds consecutive prime gaps in a jfCPAP Sieve file
      |
      > | Built & designed on Sept 22-24 & Oct 27, by Jim Fougeron.
      |
      > | Free usage granted to all. Uses the GMP large math library
      |
      > +-------------------------------------------------------------------
      +
      >
      > Gap is 2000
      > Loading data from file 'nude' ...
      > File nude loaded. 109872444 values left, sieved to: 752500739
      > Looking for gaps >= 2000 from 2^116+1 to 2^116+4000000001
      > 4598117 prp chks, tested 2080800 gaps, k=3998697975 [4052.6 prps/s]
      >
      > Time used 1135 seconds
      >
      > D:\matikka\primegaps\speedtest>
      >
      > --klip --- klip --
      >
      > So it took 15 + 19 min to check that range.

      There is probably at least another minute added in for the file I/O.
      Even with the compression in the saved files, writing the 75mb file
      (your 109 million items will produce a file about this size), and
      then re-reading it in (along with testing each and every bit to write
      the file, and then resetting them upon re-reading) takes some time.
      I would say probably 35s to save and 25s to read for this size (on a
      P450) is probably close to reality.

      >I used my P450 at home.
      > When I earlier mentioned some numbers I used more that one
      computer. Clock
      > time was
      > one day, but more than 10 cpu days.
      >
      > about 170 billion k's per day using my P450.
      >
      > Nuutti Kuosa
      >
      > -----Original Message-----
      > From: Phil Carmody [mailto:fatphil@a...]
      > Sent: 1. marraskuuta 2001 21:23
      > To: primenumbers@y...
      > Subject: [PrimeNumbers] How fast is a brute force prime gap hunt?
      >
      >
      > Just a quick question, what speed are people getting out of Jim's
      > Gapper/CPAP combo? I remember seeing something like a search of
      1100 billion
      > being mentioned in the last few days, but how long do such searches
      take?
      > I've come up with some super-carmody-bogosity heuristic
      algorithmettes, and
      > am wondering whether I should give up now, or pursue them.
      > I can scale CPU/MHz in my head. Anyone want to offer some figures?
      (And
      > sorry, no I don't have an x86 machine I can try it on myself
      presently,
      > which would appear to be the easiest way to find out.)
      > Phil
      >
      > Mathematics should not have to involve martyrdom;
      > Support Eric Weisstein, see http://mathworld.wolfram.com
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