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19081Re: [PrimeNumbers] probability of (2*p1*p2) + 1 being prime

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  • Phil Carmody
    Sep 9, 2007
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      --- 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.


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