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

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• 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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