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Re: Largest CPAP differences

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  • 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 1 of 6 , Dec 30 9:29 PM
      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 2 of 6 , Dec 31 7:03 AM
        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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