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

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• ... Good catch, Jack! Phil () ASCII ribbon campaign () Hopeless ribbon campaign / against HTML mail / against gratuitous bloodshed
Message 1 of 6 , Sep 14, 2007
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--- 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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• ... All 4 above posts were mailed September 9 but it took 5 days to deliver the posts by Jack and I. We are far apart and the posts showed up the same minute
Message 2 of 6 , Sep 14, 2007
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September 9 jtrjtrjtr2001 wrote:
> y = (2*p1*p2) + 1.

Phil Carmody wrote:
> > Well, it's just like any arbitrary [odd] number of the same size

I wrote:
> If q is a random odd prime other than p1 and p2,
> then q does not divide y-1

Jack Brennen wrote:
> And y is not congruent to 1 mod 3, or to 1 mod 5,
> or to 1 mod 7, etc.

All 4 above posts were mailed September 9 but it took 5 days to
deliver the posts by Jack and I. We are far apart and the posts
showed up the same minute so it seems like a Yahoo problem.
http://tech.groups.yahoo.com/group/primeform/message/8788 was delayed
from August 31 to September 5. Maybe the problem from