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Re: certification of a prime gap

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  • d.broadhurst@open.ac.uk
    Jose Luis Gomez Pardo wrote ... The snappy pace of 8342 bits in 66 hours (1GHz Athlon) in http://groups.yahoo.com/group/primenumbers/message/2259 is about as
    Message 1 of 12 , Aug 31, 2001
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      Jose Luis Gomez Pardo wrote

      > I realize now that the certification of the top and
      > bottom requires much more work than what I had assumed
      > from earlier David comments.

      The snappy pace of 8342 bits in 66 hours (1GHz Athlon) in

      http://groups.yahoo.com/group/primenumbers/message/2259

      is about as fast as ECPP gets, to date.

      I reckon that the median Primo time (same machine) is
      about half a week at 8000 bits. One week, or even two,
      might be required if Run 3 appears, and/or there is need of
      significant backtracking after discriminant exhaustion.

      I wonder what Hans and Giovanni are doing right now?
      5k decimal digits by someone, in time for Christmas?

      In my bones I feel that, *within operational limits*,
      Primo scales more like digts^4 than the asymptotic
      estimate digits^6. If 2.5k digits takes half a week,
      5k digits might take only only 2 or 3 months,
      on a wing and a prayer...

      David
    • Hans.Rosenthal@t-online.de
      David Broadhurst wrote: [Snip] ... Some less digits from me and some more digits from Giovanni (and from someone else) seem to be likely before Christmas :)
      Message 2 of 12 , Sep 1, 2001
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        David Broadhurst wrote:

        [Snip]
        > I wonder what Hans and Giovanni are doing right now?
        > 5k decimal digits by someone, in time for Christmas?

        Some less digits from me and some more digits from Giovanni
        (and from someone else) seem to be likely before Christmas :)

        > In my bones I feel that, *within operational limits*,
        > Primo scales more like digts^4 than the asymptotic
        > estimate digits^6. If 2.5k digits takes half a week,
        > 5k digits might take only only 2 or 3 months,
        > on a wing and a prayer...

        In my bones I'm feeling the same, but too much depends on the
        *individual* number being tested. You'll know what a certain
        5k-+ number takes to be proven prime with Tx/Po on a certain
        PC using certain methods this year, that's for sure.

        Hans

        PS: I indeed don't know what Giovanni is testing at present,
        I only know what I am working on with Primo.
      • Nathan Russell
        On Thu, 30 Aug 2001 21:30:16 -0400, Nathan Russell ... Now finished. cert_val quick-check passed, though i didn t clean out all the headers and didn t change
        Message 3 of 12 , Sep 12, 2001
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          On Thu, 30 Aug 2001 21:30:16 -0400, Nathan Russell
          <nrussell@...> wrote:

          >On Thu, 30 Aug 2001 18:35:11 -0000, d.broadhurst@... wrote:
          >
          >>Jose Luis Gomez Pardo asked about the certification
          >>of the top and bottom PrPs for his gap.
          >>My experience is that a 8000 bit PrP takes
          >>between 3 and 4 days to certify, running
          >>Primo on a 1GHz Athlon, if the chain of elliptic
          >>curves never hits "Run 3". So with a bit of luck
          >>Jose Luis' gap could be certified in a week.
          >>I have no spare machine, at present, but I think
          >>that someone here surely has! (Greg?)
          >>The top and bottom would then be archivable as
          >>ECPP primes, for a while.
          >>David
          >
          >I will do the bottom prime of this gap, devoting my P3-600 with Win98
          >and 384 MB of 133 MHz memory completely to it until it is finished.

          Now finished.

          cert_val \quick-check passed, though i didn't clean out all the
          headers and didn't change any test numbers. I don't know if that's
          important to anyone...

          I'm running a full cert_val now, and I'll send out the certificate (in
          compressed form, of course) to Jose and anyone else who expresses an
          interest after that passes. It's about 2/3 of a megabyte.

          Nathan
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