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Topic: Are these numbers always prime?
Replies: 3   Last Post: Nov 21, 2000 5:33 PM

 Messages: [ Previous | Next ]
 r3769 Posts: 30 Registered: 12/12/04
Re: Are these numbers always prime?
Posted: Nov 19, 2000 5:14 PM

r3769 wrote:

>Suppose n and b are positive integers. Set x[0]=(n-1)/n and recursively
>compute:
>
> x[i+1]=x[i]*ceil(b*x[i])-b

I meant to write: x[i+1]=x[i]*ceil(b/x[i])-b

>
>until x[i+1]=0.
>
>Now set l(b,n)=i+1. For example, l(2291,11)=10.
>
>Empirical evidence suggests: if l(b0,n)=n-1 then there exists a c0 s.t.
>l(b0+c0*k,n)=n-1 for k>0.
>
>Examples:
> l(423953,17)=16, c0=720720
> l(2579419,19)=18, c0=17*720720
> l(30364247,23)=22, c0=19*17*720720
>
>Consider the set Q={n:l(b,n)=n-1 for some b}. Are these numbers always
>prime?

Yes, of course. What I wanted to ask was if all primes are in Q.

R.

Date Subject Author
11/19/00 r3769
11/19/00 r3769
11/20/00 Hugo van der Sanden
11/21/00 r3769