whoa, I got a lot of responses!; didn't have time to look at any of them.

I made the correction to the typo earlier, but sent the e-mail to myself;

this proof makes it rock solid with the typo displayed and supplying the

proof... hope no one's mad; do you like it PROFESSOR Caldwell ??? your

website is immense if nothing else... done with maths for a while...

Professor Caldwell, et. al.

I couldn't resist... here's my idea for proof:

theorem: iff F(n)== -1 mod (2^(n-1) +1), then F(n) is prime!

if F(n)== -1 mod (r +1), then r= 2^h >1 and (r+1)*b= F(n) +1;

so, if (r +1)*b = 2^(2^n)+2, then b must equal 2; so, r +1=

2^(2^n-1) +1 implies... 2^h= 2^(2^n -1) implies... h= 2^n -1;

and if 2^n is replaced by n, then 2^n -1 is rel. prime to n-1.

now, (2^(n-1) +1) is mutually exclusive with (2^(2^n -1) +1),

and thus, if both modulators produce the same result, then

iff F(n)== -1 mod (2^(n-1) +1), then F(n) is prime; the other

case of (r -1) would be proved similarly.

*QED

I noticed it in an hour the night before & proved it last night.

Bill

--- On Wed, 11/11/09, leavemsg1 <leavemsg1@...> wrote:

> From: leavemsg1 <leavemsg1@...>

> Subject: Re: Fermat conjecture; please post it

> To: "Bill Bouris" <leavemsg1@...>

> Date: Wednesday, November 11, 2009, 9:16 AM

> small typo... look below.

>

> --- In primenumbers@yahoogroups.com,

> Bill Bouris <leavemsg1@...> wrote:

> >

> > Hello, Professor Caldwell.

> >

> > I like your website. Could you please post the

> following conjecture:

> >

> > if n>= 2 and F(n)= 2^(2^n)+1, then iff [F(n) mod

> (2^(n-1)+1) == -1]

> >

> > (or) [F(n) mod (2^(n-1)+1) == -1], then F(n) is

> prime.

>

> the second half should read ... F(n) mod (2^(n-1)-1) == -1;

> sorry.

>

> >

> >

> > it requires someone as formidable as Lucas, Lehmer,

> etc. to prove it.

> >

> > examples...

> > n= 2; F(n)= 17; 17 mod 3 == -1; 17 mod 1 == 0; 17 is

> prime!

> >

> > n= 3; F(n)= 257; 257 mod 5 == +2; 257 mod 3 == -1;

> 257 is prime!

> >

> > n= 4; F(n)= 65537; 655377 mod 9 == -1; 65537 mod 7 ==

> +3; 65537 is prime!

> >

> > n= 5; F(n)= 4294967297; F(n) mod 17 == +2; F(n) mod 15

> = +2; composite!

> >

> > I wish someone had the technical expertise to prove

> it; it's valid, and

> > I've studied it... trying to come up with a

> proof. Share it with a close

> > colleague, if you like.

> >

> > Thanks in advance,

> >

> > Bill Bouris

> >

>

>

>