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## Re: sufficent proof for primes of the kind p:=x^2+x+1

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• ... as ... But p=241 is not congruent to 3 (mod 4). So it is not a counter- example. Best regards, Dario Alpern Buenos Aires - Argentina
Message 1 of 3 , Dec 13, 2006
--- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>
wrote:
>
> --- In primenumbers@yahoogroups.com, "Bernhard Helmes" <bhelmes@>
> wrote:
> >
> > A beautifull evening,
> >
> > I try to give you a sufficent proof for primes p:=x^2+x+1
> >
> > p:=x^2+x+1=x*(x+1)+1 with p = 3 mod 4 => 2 appears only one time
as
> > divisor of p-1
> > p mod 3 = 1 or in other words 3 | p-1
> > p mod 9 > 1 => 3 appears only one time as divisor of p-1
> >
> > 2 ^ ((p-1)/2) = p-1 mod p, must be verified
> >
> > then p is prime
> >
>
> Hi, Bernhard.
> I think that x=15 is a counter-example... 2^((240/2)) == 1 mod 241.
> Is it? Bill
>

But p=241 is not congruent to 3 (mod 4). So it is not a counter-
example.

Best regards,

Dario Alpern
Buenos Aires - Argentina
http://www.alpertron.com.ar/ENGLISH.HTM
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