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Re: [PrimeNumbers] verification

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  • 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 1 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/
      >


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