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Re: [PrimeNumbers] Please help....

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  • Andy Swallow
    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
      reply...

      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
      > IIITAllahabad
      > http://profile.iiita.ac.in
    • Jens Kruse Andersen
      ... 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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