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• Dear idiot, 2KP+1 is an arithmetic progression whose elements have no common factor, and so will always contain infinitely many primes, whatever P is. Andy PS
Message 1 of 4 , Mar 7, 2004
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Dear idiot,

2KP+1 is an arithmetic progression whose elements have no common factor,
and so will always contain infinitely many primes, whatever P is.

Andy

PS Don't take offence to the dear idiot start, but if you're going to
ask for help by saying 'dear geeks', then you can probably expect such a

PPS See Dirichlet's theorem, in any good number theory book, for more
information.

On Sun, Mar 07, 2004 at 08:00:17AM -0800, Shiv Nandan Singh wrote:
> Dear geeks ,
> Are there any primes P of any form such that 2*K*P + 1 is never prime
> for any positive value of K. Or to be specific does there exist any
> single prime P such that 2*KP + 1 is never prime for all K>0 .Or could
> you prove its inexistence....? Any light on the issue would be highly
> praised....
> Thanks
> Shiv Nandan Singh
> http://profile.iiita.ac.in
• ... 2*P and 1 are relatively prime (whether P is prime or not). Then Dirichlet s theorem says there are always infinitely many primes.
Message 2 of 4 , Mar 7, 2004
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Shiv Nandan Singh wrote:
> Are there any primes P of any form such that 2*K*P + 1 is never prime for
> any positive value of K.

2*P and 1 are relatively prime (whether P is prime or not).
Then Dirichlet's theorem says there are always infinitely many primes.
http://primes.utm.edu/glossary/page.php?sort=DirichletsTheorem

--
Jens Kruse Andersen
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