Loading ...
Sorry, an error occurred while loading the content.
 

Re: Probable factorization of 3 consecutive 60222-digit integers

Expand Messages
  • Jens Kruse Andersen
    ... Thanks. And thanks to Chris Caldwell for maintaining The Prime Database. It contains n/2 = 38602791*2^200025-1, by Jiong Sun in 2004:
    Message 1 of 5 , Sep 14, 2007
      David Broadhurst wrote:
      > Congrats to Jens for
      > n+1 = 577849*2645749*3427009*prp60203
      > at
      > http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm

      Thanks.

      And thanks to Chris Caldwell for maintaining The Prime Database.
      It contains n/2 = 38602791*2^200025-1, by Jiong Sun in 2004:
      http://primes.utm.edu/primes/page.php?id=69628

      If x and x+1 are completely factored then 3 consecutive
      factorizations are achieved if x-1, x+2 or 2x+1 can be factored.

      prp60203 = (38602791*2^200026-1)/(577849*2645749*3427009)
      was found with the POWMOD script command in
      PFGW Version 20050213.Win_Dev (Alpha/IBDWT 'caveat utilitor')

      If the product of known factors in m is f then this POWMOD can be
      used to make a prp test of m/f as fast as of m when m is an optimized
      form.
      It reduced prp time of prp60203 from 217s with PFGW Version 1.2.0 to
      78s.
      This advantage is so great that I only examine known primes of form
      k*2^n+-1 . All 3 candidates for prp testing can be written as
      cofactors of a number which is also of the optimized form k*2^n+-1.

      There is obviously no plan to prove prp60203.

      --
      Jens Kruse Andersen
    • David Broadhurst
      ... Ah, if only I could get that irrational base discrete weighted transform running under linux ... David
      Message 2 of 5 , Sep 15, 2007
        --- In primeform@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>
        wrote:

        > prp60203 = (38602791*2^200026-1)/(577849*2645749*3427009)
        > was found with the POWMOD script command in
        > PFGW Version 20050213.Win_Dev (Alpha/IBDWT 'caveat utilitor')

        Ah, if only I could get that irrational base discrete
        weighted transform running under linux ...

        David
      • David Broadhurst
        ... But there was plan to improve on that probable factorization: http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm ... Perhaps this trawl will
        Message 3 of 5 , Sep 15, 2007
          --- In primeform@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>
          wrote:

          > There is obviously no plan to prove prp60203.

          But there was plan to improve on that probable factorization:

          http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm
          > n-1 = 3^2*11*13*22091*417293*c64854

          Perhaps this trawl will run, and run, making Jens
          update his own k=3 record at frequent intervals?

          David
        • Jens Kruse Andersen
          ... You mailed 18 minutes after the record was added. That was fast! The hit was prp64853 = (3045*2^215472-2)/(2*17*1151*27067*173473). Chris Chatfield found
          Message 4 of 5 , Sep 15, 2007
            David Broadhurst wrote:
            > "Jens Kruse Andersen" wrote:
            >
            >> There is obviously no plan to prove prp60203.
            >
            > But there was plan to improve on that probable factorization:
            >
            > http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm
            >> n-1 = 3^2*11*13*22091*417293*c64854

            You mailed 18 minutes after the record was added. That was fast!
            The hit was prp64853 = (3045*2^215472-2)/(2*17*1151*27067*173473).
            Chris Chatfield found 3045*2^215472-1 in 2005:
            http://primes.utm.edu/primes/page.php?id=75494

            > Perhaps this trawl will run, and run, making Jens
            > update his own k=3 record at frequent intervals?

            It's still running. For how long is not decided, and there are
            probably only few hits left on known primes.
            I don't expect to search above the ongoing twin prime search at
            k*2^333333+/-1 - at least not before they actually find a twin and set
            a record. By then there will also be a Chen prime record to retake...

            --
            Jens Kruse Andersen
          Your message has been successfully submitted and would be delivered to recipients shortly.