Loading ...
Sorry, an error occurred while loading the content.
 

Re: Lucas super-pseudoprimes for Q <> 1

Expand Messages
  • djbroadhurst
    Mike had difficulty posting and asked me to post this for him: ... Yes. Here is my function of 3Nov10:- { is_eligible(n)= local(f,ind,p,res=1); f=factor(n);
    Message 1 of 46 , Nov 7, 2010
      Mike had difficulty posting and asked me to post this for him:

      =======

      > Is the above, in essence, your conjectural method?

      Yes.

      Here is my function of 3Nov10:-
      {
      is_eligible(n)=
      local(f,ind,p,res=1);
      f=factor(n);
      for(ind=1,#f[,1],
      if(f[ind,2]>1,res=0;break(1)); \\not squarefree
      p=f[ind,1];
      if( ((n-1)%(p-1))<>0,
      if( !((((n-1)%(p+1))==0)&&(((n+1)%(p-1))==0)),res=0;break(1));
      ); \\end if
      ); \\end for ind
      res;
      }

      Now, how to prove this is kosher?...

      Mike

      =====

      I have already posted the "sufficient" part of the proof.
      The "necessary" part is awaited ...

      David (pp Mike)
    • djbroadhurst
      ... http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out gives my 116, in the format [n, factors, number of solutions] With n
      Message 46 of 46 , Nov 9, 2010
        --- In primenumbers@yahoogroups.com,
        "mikeoakes2" <mikeoakes2@...> wrote:

        > > My revised count up to 2*10^10 is 116.
        > My (original) count up to 2*10^10 was 105.
        > So it must have missed 11, i.e. a bigger proportion.

        http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out
        gives my 116, in the format [n, factors, number of solutions]

        With n < 2*10^10, the record-holder for the number of solutions is
        [2214495361, [13, 17, 23, 29, 83, 181], 147407]
        which googles quite nicely, linking to
        http://www.cs.rit.edu/usr/local/pub/pga/fibonacci_pp

        David
      Your message has been successfully submitted and would be delivered to recipients shortly.