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verification

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  • Payam Samidoost
    ... Thanks Jim. Your comment clearly shows the need for the verification of the results. ... My suggestion for the verification of the Sierpinski problem
    Message 1 of 5 , May 14, 2002
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      Jim Fougeron have kindly noted me:

      > It appears that you missed 2^16389+67607 somehow.

      Thanks Jim. Your comment clearly shows the need for the verification of the
      results.

      ---------------------------------------------------
      My suggestion for the verification of the Sierpinski problem results:

      The recently developed project SB (Seventeen or Beast) by Louis Helm and
      David Norris at http://sb.pns.net/ with its current (Slow but Beautiful ;o)
      implementation is not at all appropriate for the research specially for the
      huge exponents. Instead IT IS IDEAL for verification of the results with
      small exponents and old machines.

      Louis Helm and David Norries: What is your idea?

      If the SB implementation will change such that it could compete with George
      Woltman's remarkable PRP then I would certainely close my project at
      http://sierpinski.insider.com/4847 and happily join them.

      Payam
    • Devaraj Kandadai
      In my presentation of “Minimum Universal exponent generalisation of Fermat s theorem” at the Hawaii Intl conference in 2006 I had stated that 31 is a
      Message 2 of 5 , Jun 2, 2009
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        In my presentation of �Minimum Universal exponent generalisation of Fermat's
        theorem� at the Hawaii Intl conference in 2006 I had stated that 31 is a
        factor of the following and that 127, 157 and 8191 are not factors :



        2^97500641752017987211 + 29.


        Can anyone verify this by PFGW pl?
        Devaraj


        [Non-text portions of this message have been removed]
      • Alan Eliasen
        ... I didn t use PFGW, but it s easy to test. In short, your statement is correct. The two smallest factors are 31 and 817469483. If you want to
        Message 3 of 5 , Jun 2, 2009
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          Devaraj Kandadai wrote:
          > In my presentation of “Minimum Universal exponent generalisation of Fermat's
          > theorem” at the Hawaii Intl conference in 2006 I had stated that 31 is a
          > factor of the following and that 127, 157 and 8191 are not factors :
          >
          > 2^97500641752017987211 + 29.
          >
          > Can anyone verify this by PFGW pl?

          I didn't use PFGW, but it's easy to test. In short, your statement
          is correct. The two smallest factors are 31 and 817469483. If you want
          to exhaustively find more factors, the following simple program should help:

          Frink program below: ( http://futureboy.us/frinkdocs/ )
          --------------------------------------------------

          test[p] := (modPow[2,97500641752017987211,p]+29) mod p

          n = 1
          do
          {
          n = nextPrime[n]
          if test[n] == 0
          print[n + " "]
          } while true

          -----------------------------------------------------

          See the thread in this group 'Checking Large "Prime Numbers"?'
          beginning on 2006-05-08 for related GP/PARI scripts that can be modified
          to find other factors.

          --
          Alan Eliasen
          eliasen@...
          http://futureboy.us/
        • Devaraj Kandadai
          Thank you very much; my knowledge of programming is limited to some elementary programming in pari. My approach is purely mathematical. By this I can find
          Message 4 of 5 , Jun 2, 2009
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            Thank you very much; my knowledge of programming is limited to some
            elementary programming in pari. My approach is purely mathematical. By this
            I can find some factors and non-factors of very large numbers with an
            exponential shape (like the number I had asked about).
            Thanking u once again,
            Devaraj



            On Tue, Jun 2, 2009 at 1:35 PM, Alan Eliasen <eliasen@...> wrote:

            > Devaraj Kandadai wrote:
            > > In my presentation of �Minimum Universal exponent generalisation of
            > Fermat's
            > > theorem� at the Hawaii Intl conference in 2006 I had stated that 31 is a
            > > factor of the following and that 127, 157 and 8191 are not factors :
            > >
            > > 2^97500641752017987211 + 29.
            > >
            > > Can anyone verify this by PFGW pl?
            >
            > I didn't use PFGW, but it's easy to test. In short, your statement
            > is correct. The two smallest factors are 31 and 817469483. If you want
            > to exhaustively find more factors, the following simple program should
            > help:
            >
            > Frink program below: ( http://futureboy.us/frinkdocs/ )
            > --------------------------------------------------
            >
            > test[p] := (modPow[2,97500641752017987211,p]+29) mod p
            >
            > n = 1
            > do
            > {
            > n = nextPrime[n]
            > if test[n] == 0
            > print[n + " "]
            > } while true
            >
            > -----------------------------------------------------
            >
            > See the thread in this group 'Checking Large "Prime Numbers"?'
            > beginning on 2006-05-08 for related GP/PARI scripts that can be modified
            > to find other factors.
            >
            > --
            > Alan Eliasen
            > eliasen@...
            > http://futureboy.us/
            >


            [Non-text portions of this message have been removed]
          • Devaraj Kandadai
            In fact if n is the exponent in 2^n + 29, any value of n ending in 1 or 6 is divisible by 31. This has something to do with group theory. Devaraj ...
            Message 5 of 5 , Jun 3, 2009
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              In fact if n is the exponent in 2^n + 29, any value of n ending in 1 or 6
              is divisible by 31. This has something to do with group theory.
              Devaraj

              On Tue, Jun 2, 2009 at 1:35 PM, Alan Eliasen <eliasen@...> wrote:

              > Devaraj Kandadai wrote:
              > > In my presentation of �Minimum Universal exponent generalisation of
              > Fermat's
              > > theorem� at the Hawaii Intl conference in 2006 I had stated that 31 is a
              > > factor of the following and that 127, 157 and 8191 are not factors :
              > >
              > > 2^97500641752017987211 + 29.
              > >
              > > Can anyone verify this by PFGW pl?
              >
              > I didn't use PFGW, but it's easy to test. In short, your statement
              > is correct. The two smallest factors are 31 and 817469483. If you want
              > to exhaustively find more factors, the following simple program should
              > help:
              >
              > Frink program below: ( http://futureboy.us/frinkdocs/ )
              > --------------------------------------------------
              >
              > test[p] := (modPow[2,97500641752017987211,p]+29) mod p
              >
              > n = 1
              > do
              > {
              > n = nextPrime[n]
              > if test[n] == 0
              > print[n + " "]
              > } while true
              >
              > -----------------------------------------------------
              >
              > See the thread in this group 'Checking Large "Prime Numbers"?'
              > beginning on 2006-05-08 for related GP/PARI scripts that can be modified
              > to find other factors.
              >
              > --
              > Alan Eliasen
              > eliasen@...
              > http://futureboy.us/
              >


              [Non-text portions of this message have been removed]
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