- Devaraj Kandadai wrote:
> In my presentation of “Minimum Universal exponent generalisation of Fermat's

I didn't use PFGW, but it's easy to test. In short, your statement

> 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?

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/ - 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] - 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]