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[PrimeNumbers] Re: Largest CPAP differences

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  • Jens Kruse Andersen
    ... I also chose to search an easy improvement with a special d: 46313478 * 1201#/1302643 + x498 + 2310n, for n = 0..3 Using the special crafted x498 at the
    Message 1 of 6 , Dec 3, 2004
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      Jim Fougeron wrote:

      > I have a 2004 addition for CPAP-4 (yes, it was very easy to find)
      >
      > 78006074.883#+k*2004+R is prime for k = [0...3]
      >
      > Using the special crafted R of:
      >
      > R=211456......
      >
      > This is 379 decimal digit CPAP-4 with d=2004 (d chosen for the
      > year of finding).

      I also chose to search an easy improvement with a "special" d:

      46313478 * 1201#/1302643 + x498 + 2310n, for n = 0..3

      Using the special crafted x498 at the site.

      d = 2310 = 11# is the smallest possible d for a CPAP-11.
      Only 7 more primes and a few trillion GHz years to go!
      (Yes, I checked the CPAP-4 doesn't extend)

      PrimeForm/GW prp'ed and Marcel Martin's Primo proved.
      This record is going fast. I added a record history to keep up:
      http://hjem.get2net.dk/jka/math/cpap.htm#difference_history

      --
      Jens Kruse Andersen
    • jim_fougeron
      I have followed Jens lead, and on Christmas day, discovered a CPAP-5 with a gap of 2310. This number is: 9400734826*1499#+x632+2310n with n from 0 to 4 and
      Message 2 of 6 , Dec 30, 2004
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        I have followed Jens lead, and on Christmas day, discovered a
        CPAP-5 with a gap of 2310. This number is:

        9400734826*1499#+x632+2310n

        with n from 0 to 4 and

        x632 = 29453397765450271545399188085266
        55368252378620585099496385650600431498269661083903
        16211042912735310776015757228962737061429256177227
        59452435429488328389328281466289664367352954006161
        79207095576921259775792175026579617936878099659414
        32837668975308693630297479962123616982055909919099
        17025496933775418577095695897932136276184735064982
        12549583475520940170609152997656163627242028405951
        20483292467767923352271563327090757509953181908766
        84457108535835673100713235902439791043089273743933
        82074800677693506138530042890392327727580262290580
        36426781990814418117965800120148977404531919575260
        38333320588240996195703518136355252551601080488639

        Now, we need a CPAP-6 :) Any takers?

        Jim.


        --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
        <jens.k.a@g...> wrote:
        > Jim Fougeron wrote:
        >
        > > I have a 2004 addition for CPAP-4 (yes, it was very easy to find)
        > >
        > > 78006074.883#+k*2004+R is prime for k = [0...3]
        > >
        > > Using the special crafted R of:
        > >
        > > R=211456......
        > >
        > > This is 379 decimal digit CPAP-4 with d=2004 (d chosen for the
        > > year of finding).
        >
        > I also chose to search an easy improvement with a "special" d:
        >
        > 46313478 * 1201#/1302643 + x498 + 2310n, for n = 0..3
        >
        > Using the special crafted x498 at the site.
        >
        > d = 2310 = 11# is the smallest possible d for a CPAP-11.
        > Only 7 more primes and a few trillion GHz years to go!
        > (Yes, I checked the CPAP-4 doesn't extend)
        >
        > PrimeForm/GW prp'ed and Marcel Martin's Primo proved.
        > This record is going fast. I added a record history to keep up:
        > http://hjem.get2net.dk/jka/math/cpap.htm#difference_history
        >
        > --
        > Jens Kruse Andersen
      • Jens Kruse Andersen
        ... Congratulations. Thanks for your interest in the new record category. http://hjem.get2net.dk/jka/math/cpap.htm#difference is updated. Note that it is also
        Message 3 of 6 , Dec 31, 2004
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          Jim Fougeron wrote:

          > I have followed Jens lead, and on Christmas day, discovered a
          > CPAP-5 with a gap of 2310. This number is:
          >
          > 9400734826*1499#+x632+2310n
          >
          > Now, we need a CPAP-6 :) Any takers?

          Congratulations.
          Thanks for your interest in the new record category.
          http://hjem.get2net.dk/jka/math/cpap.htm#difference is updated.
          Note that it is also easily the second largest overall CPAP-5, only beaten by
          Jim himself who has the whole top-10.

          For a CPAP-6 with difference 2310, I think I would search around 560 digits.
          For comparison, the largest known 6 simultaneous primes is a 418-digit CC-6 by
          Dirk Augustin: http://hjem.get2net.dk/jka/math/simultprime.htm#records
          Around 16 AP-6's at 560 digits are expected before hitting a CPAP-6 with my
          program.

          It looks pretty hard. I estimate perhaps 5 GHz years if my deep sieve is
          improved to manage sparse forms better.
          I don't have plans to make such a hard CPAP-6 search.

          --
          Jens Kruse Andersen
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