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

Prime sequence, is it likely to be extendable

Expand Messages
  • Kevin Acres
    Whilst working on another project, I noticed a sequence of primes given by the following pari/gp script: { p=7; for(j=1,1206, i = (j*12)+9; p = 7 +
    Message 1 of 3 , Oct 9, 2013
      Whilst working on another project, I noticed a sequence of primes given by
      the following pari/gp script:

      {
      p=7;
      for(j=1,1206,
      i = (j*12)+9;
      p = 7 + ((2^i-1)*16);
      o=p-sum(x=0,(i-6)/3,4*8^(x))*32-23;
      l=lift(Mod(2,p)^o);
      if(l == 1,
      print([j,i,l,isprime(p/7),[ceil(log(p/7)/log(10))]]);
      );
      );
      }

      where p/7 is prime for j = 1, 6, 9, 13, 18, 20, 103, 151 and 1206

      My question is, is it likely that this sequence is extendable or is it
      likely to be finite?

      I've put a fair number of cycles into this, but was unable to find
      anything with j > 1206 as yet.


      Regards,

      Kevin.
    • djbroadhurst
      ... Heuristically, we expect an infinty of primes of this form: (2^(12*1+13)-9)/7 is trivially prime!: 4793489 (2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
      Message 2 of 3 , Oct 10, 2013

         ---In primenumbers@yahoogroups.com, <research@...> wrote:

        > is it likely that this sequence is extendable or is it
        > likely to be finite?
         
        Heuristically, we expect an infinty of primes of this form:
         
        (2^(12*1+13)-9)/7 is trivially prime!: 4793489
        (2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
        (2^(12*9+13)-9)/7 is 3-PRP! (0.0000s+0.1096s)
        (2^(12*13+13)-9)/7 is 3-PRP! (0.0000s+0.0605s)
        (2^(12*18+13)-9)/7 is 3-PRP! (0.0000s+0.0333s)
        (2^(12*20+13)-9)/7 is 3-PRP! (0.0000s+0.0418s)
        (2^(12*103+13)-9)/7 is 3-PRP! (0.0013s+0.0458s)
        (2^(12*151+13)-9)/7 is 3-PRP! (0.0020s+0.0860s)
        (2^(12*1206+13)-9)/7 is 3-PRP! (0.1019s+0.0397s)
        (2^(12*7269+13)-9)/7 is 3-PRP! (5.2402s+0.0563s)
        David
      • Kevin Acres
        Hello David, Thanks for the info. I hadn t spotted the 12*n+13 pattern. Best Regards, Kevin.
        Message 3 of 3 , Oct 10, 2013
          Hello David,

          Thanks for the info. I hadn't spotted the 12*n+13 pattern.


          Best Regards,

          Kevin.


          > ---In primenumbers@yahoogroups.com, <research@...> wrote:
          >
          >> is it likely that this sequence is extendable or is it
          >> likely to be finite?
          >
          > Heuristically, we expect an infinty of primes of this form:
          >
          > (2^(12*1+13)-9)/7 is trivially prime!: 4793489
          > (2^(12*6+13)-9)/7 is 3-PRP! (0.0000s+0.1175s)
          > (2^(12*9+13)-9)/7 is 3-PRP! (0.0000s+0.1096s)
          > (2^(12*13+13)-9)/7 is 3-PRP! (0.0000s+0.0605s)
          > (2^(12*18+13)-9)/7 is 3-PRP! (0.0000s+0.0333s)
          > (2^(12*20+13)-9)/7 is 3-PRP! (0.0000s+0.0418s)
          > (2^(12*103+13)-9)/7 is 3-PRP! (0.0013s+0.0458s)
          > (2^(12*151+13)-9)/7 is 3-PRP! (0.0020s+0.0860s)
          > (2^(12*1206+13)-9)/7 is 3-PRP! (0.1019s+0.0397s)
          > (2^(12*7269+13)-9)/7 is 3-PRP! (5.2402s+0.0563s)
          >
          > David
          >
        Your message has been successfully submitted and would be delivered to recipients shortly.