## Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]

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• Hello David, ... Something like [18*x-448552937, [15788701, 15]] probably violates your search criteria. I just need to know if A
Message 1 of 143 , Jan 4, 2011
Hello David,

At 07:31 AM 20/11/2010, djbroadhurst wrote:

>
> > Let A, B and L be integers with A > 1 and L > 1.
> >
> > Definition: A "Smith chain" of length L is a chain
> > p[n+1] = A*p[n] + B, such that p[n] is prime,
> > for n = 1 to L, with p[2] > p[1] > A.
>
> > Definition: A "maximal Smith chain" is a Smith chain with
> > integers (A,B) for which there is a proof that no chain
> > of greater length exists.

Something like [18*x-448552937, [15788701, 15]] probably violates

I just need to know if A < p[1] < p[2] can be stretched to A <
abs(p[1]) < abs(p[2]) or is that outside of these rules?

Best Regards,

Kevin. (with 25 conforming 15/16s)
• ... 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
Message 143 of 143 , Jan 7, 2011