<paulunderwood@...> wrote:>

I'm not mad at you Paul; I'm pissed at myself for not having a better

> --- In primenumbers@yahoogroups.com, Bill Bouris <leavemsg1@> wrote:

> >

> > Hello, Group.

> >

> > The usual Proth numbers are described as Y= n*2^k +1

> > where all 'k's are such that n < 2^k +1.

understanding of my own idea.

Yes, 'n' would need to be odd...

and Yes, 'Y' should be more conventionally restated as Y= k*2^n+1.

> >

and my "curiosity" is... that... (curiosity killed the cat,...)

> >

> > 2nd-kind Proth's are described (by me) as Z= n*2^k +1

> > where 'n' is strictly inside the range 2^k+1 < n <

> > 2*(2^k+1) for some 'k'.

> >

> >

> > My conjecture is... that...

I'm trying to discover a large prime number that may later be proven

> >

> > If 'k' is further restricted to be a prime, then

> > 2nd-kind Proth's could be detected as prime iff

> > 2^(Z-1) == 1 (mod Z)... in one single test.

> >

prime using a more proper method. (but, satisfaction brought him (the

cat) back.)

> >

I don't doubt that this statement is true.

> > In other words, when Z is 2-PRP, it would in fact be

> > prime iff 'k' is prime and n is modified as stated in

> > the above definition of a 2nd-kind Proth.

> >

> >

> > Others have informed me... that only very few 2-PRP

> > tested numbers would in fact be composite.

> >

statement...

> > My

> > again is that "NO" psuedoprimes can be

Sometimes, my own hunches... make me feel like an ice pick.

> > constructed iff 'n' is inside the range 2^k+1 < n <

> > 2*(2^k+1) and 'k' is prime.

> >

> > Any suggestions... or comments?... besides 'Stop

> > feed-ing the troll'.

> >

>

Bill

> Biting, for a start we usually talk of k*2^n+1 and not "n*2^k+1".

just

>

> I am guilty for the over use of the word "conjecture" -- some people

> would rather say "a shot in the dark". A conjecture, I suppose, must

> have some kind of basis, intimating a series of logical/mathematical

> steps or reasons that lead partially to a fully fledged theorem.

>

> The received wisdom is that conjectures such as yours have N^(1-e)

> counterexamples where "e" can be chosen as small as you like -- N

> has to very big, more often than not, bigger than we humans can ever

&&Mod(2,N)^(N-1)==1,print(k"

> calculate with all our computers,

>

> ?

> forprime(n=2,13,for(k=2^n+2,2*(2^n+1)-1,N=k*2^n+1;if(!isprime(N)

> "n" "N))))

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> 12816 13 104988673

>

> Paul

>

> > Bill Bouris, USA

> >

> >

> >

> >

>

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> >

>