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Re: FW: [PrimeNumbers] Records page.

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  • Phil Carmody
    ... Thinks out loud... GenSv? Phil ===== -- .sig selecter broken, please ignore. __________________________________________________ Do You Yahoo!? Yahoo!
    Message 1 of 2 , Feb 28, 2002
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      --- Torbjorn_Alm <torbjorn.alm@...> wrote:
      > I have been doing some search on PAP:s during the years.
      > The first attempt was don 1968, but the available computer power
      > was too expensive and too slow, even if we were on the right track.
      > (Hans Riesel, BIT 10(1970)333,342).
      >
      > Later I picked up the algorithms and made much better programs
      > along with with better computers.
      >
      > I have a nice collection of PAP:s with up to 17 terms.
      >
      > If you plot log (first term) aginst number of terms, it is fairly
      > straight. An extrapolation indicates that the first term for
      > PAP23 would be about 4*10^13 and for PAP24 would be about 2*10^14.
      >
      > The sieve eliminates all numbers without 14 terms with no factor
      > below 400. It means that only every 5000 needs to be tested
      > extensivly. The current speed is 10^10 per hour on a 850 PIII.

      Thinks out loud...

      GenSv?

      Phil

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      .sig selecter broken, please ignore.

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    • Torbjorn Alm
      I have been doing some search on PAP:s during the years. The first attempt was don 1968, but the available computer power was too expensive and too slow, even
      Message 2 of 2 , Mar 1, 2002
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        I have been doing some search on PAP:s during the years.
        The first attempt was don 1968, but the available computer power
        was too expensive and too slow, even if we were on the right track.
        (Hans Riesel, BIT 10(1970)333,342).

        Later I picked up the algorithms and made much better programs
        along with with better computers.

        I have a nice collection of PAP:s with up to 17 terms.

        If you plot log (first term) aginst number of terms, it is fairly
        straight. An extrapolation indicates that the first term for
        PAP23 would be about 4*10^13 and for PAP24 would be about 2*10^14.

        The sieve eliminates all numbers without 14 terms with no factor
        below 400. It means that only every 5000 needs to be tested
        extensivly. The current speed is 10^10 per hour on a 850 PIII.



        -----Original Message-----
        From: Paul Jobling [mailto:Paul.Jobling@...]
        Sent: den 28 februari 2002 14:41
        To: 'Phil Carmody'; 'primenumbers'
        Subject: RE: [PrimeNumbers] Records page.


        > > This is a very long standing record (1990ish as I recall, by
        > > Pritchard et al),
        > > and my feeling also is that a little brainpower and a lot of
        > > computing power
        > > could see this fall...
        >
        > IIRC 1995, it was the output of an entire computer-lab full of
        > computers. Moore's law says that 1995 was a long time ago, but even a
        > bench of modern top of the range machines can't compete with an
        > entire lab of 1995 machines. (Depending on lab size, of course)

        I just looked, the Math.Comp. article is 1995, so the AP was probably found
        a
        couple of years earlier. And indeed, a little more Googling shows that it
        was
        found in March 1993 using ~60 computers.

        Their earlier search found APs of length 19, using 14000 hours of CPU on a
        couple of VAX-11/780's in 1983. Would anybody care to speculate/calculate
        how
        many hours of 2GHz Intel/AMD CPU that is the equivalent of?

        And by the way, I did say "a lot of computing power", so that should cover
        my
        tracks!

        Regards,

        Paul.


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