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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 ...
Message 1 of 5 , Jun 3 8:06 PM
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:

> > 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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