Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]
- --- On Mon, 1/3/11, djbroadhurst <d.broadhurst@...> wrote:
> --- In firstname.lastname@example.org,You're being willed on from here in Estonia, too, Kevin!
> Kevin Acres <research@...> wrote:
> > I expect this to give an extra 6 or so 15/16 chains on
> > top of the 18 I have now.
> The bad news, of course, is that Poisson gives you
> no credit whatsoever for the 18 previous failures.
> Your chance of success with the next 6 is about
> 1 - exp(-6*mu) =~ 50%
> if we are are right about the mean probability
> mu =~ 1/9.
> Good luck!
I always like to believe that the same kind of influence that sticks the e^-gamma term into prime density expressions is kind enough to violate the Poisson independence criterion too.
- --- In email@example.com,
Kevin Acres <research@...> wrote:
> x=a*x+b either is a square or has a square as a major factor.Suppose that we want to start with a square and get a square.
Then we must solve the Diophantine equation
y^2 = a*x^2 + b
For any pair (a,b), Dario will tell us all the solutions: