Re: Prime chains x-->Ax+B
- --- In email@example.com, "djbroadhurst" <d.broadhurst@...> wrote:
>That's a really neat script, and (after formatting it properly:-) I believe it.
> > asking that
> > N = 3^t+4
> > M = (N-2)*(N-3)+3
> > be simultaneously prime. The Poisson mean for
> > such cases with t > x >> 1 may be estimated as
> > C/(2*log(3)^2)*sum(t>x,1/t^2) =~ C/(2*log(3)^2)/x
> > where C is a constant of order unity.
> Sieving to depth 10^8, with the aid of "znorder" and
> "polrootsmod" in Pari-GP, I estimated
> C ~ 6.5, but the convergence is not good:
> [7.6000, 11]
> [7.4962, 101]
> [7.4031, 1009]
> [7.5940, 10007]
> [7.2959, 100003]
> [7.0154, 1000003]
> [6.7590, 10000019]
> [6.5402, 100000007]
> David (puzzled by this slow convergence)
But you were clearly running 64-bit pari, since
> default(realprecision,5);gives only 9-digit precision in 32-bit pari, and that's not accurate enough.
To make the code portable, you should have written something like
I have gone up to nextprime(4*10^9) and have 2 new points for you:-
Convergence still slow.
- --- In firstname.lastname@example.org,
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: