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19088Re: [PrimeNumbers] probability of (2*p1*p2) + 1 being prime

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  • Phil Carmody
    Sep 14, 2007
      --- Jack Brennen <jb@...> wrote:
      > Phil Carmody wrote:
      > > --- jtrjtrjtr2001 <jtrjtrjtr2001@...> wrote:
      > >> Hi,
      > >>
      > >> Let p2 be a large prime. We find another large random prime p1, such that
      > >> y = (2*p1*p2) + 1.
      > >>
      > >> Is there any way, one could quantify the probability of y being a prime?
      > >
      > > Well, it's just like any arbitrary number of the same size except that
      > > it's even, it's not divisible by p1, and it's not divisible by p2.
      > > Therefore there's a prime density boost of (2/1) * (p1/(p1-1)) *
      > (p2/(p2-1))
      > > Those final two factors are effectively 1.
      > >
      >
      > And y is not congruent to 1 mod 3, or to 1 mod 5, or to 1 mod 7, etc.

      Good catch, Jack!

      Phil

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