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Re: [PrimeNumbers] verification

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  • 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 1 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 2 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 3 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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