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10649Re: primes close to 2^(2^n) for n = 11..14

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  • jim_fougeron <jfoug@kdsi.net>
    Jan 4, 2003
      --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@y...>
      wrote:
      > --- Carl Devore <devore@m...> wrote:
      >>
      >> On Fri, 3 Jan 2003, Phil Carmody wrote:
      >>>I don't know any list which goes up to such high powers of 2.
      >>>Heheh, 2^(2^9) I could give you a vast number of examples for.
      >>
      >>I found a list for the largest n-bit prime for n up to 400. It
      >>should be feasible, and useful I believe, to extend this up
      >>n~2^14. Even a list of any n-bit prime for each n would be useful.
      >
      >This is a job for script-mode PFGW. Anyone care to write a script
      >that will generate 10 PRPs above and below each exponent?
      >(You only need script mode to get it to stop after finding 10, you
      >could> simply get it to to a fixed size band using ordinary ABC2
      >mode.)

      That is a pretty slow way to do it. Might I suggest using CPAPSieve
      to presieve. It operates as fast (or nearly as fast) as NewPGen.
      Once the sieved file is generated (in ABC or ABCD format, not ABC2)
      Then, once the well factored data is built, use PFGW to process the
      file. Stop (manually) when 10 (or more) primes have been found.

      This method should allow a much faster search than using the ABC2
      format and using PFGW to trial factor each candidate individually.

      If anyone wants to do this, I have a newer version of CPAPSieve that
      can do b^n-K as well as b^n+K factoring (and a program called reverse
      that reverses the -maxK to -minK file so that the number closer to
      k==0 are tested first).

      If anyone wants to do this, contact me off list. I might be hard to
      get ahold of this weekend (will be out hunting), but I can get you
      a newer version of CPAPSieve (the version on-line will work for the
      b^n+K testing), and a version of reverse.exe (simple text file line
      reversing program).

      Jim.

      PS, here are some results (these are ONLY prp-3 tested):

      2^2048+981
      2^2048+1617
      2^2048+3063
      2^2048+3211
      2^2048+4143
      2^2048+7405
      2^2048+9843
      2^2048+10665
      2^2048+10725
      2^2048+11097
      2^2048+11467

      2^2048-1557
      2^2048-2543
      2^2048-7437
      2^2048-8507
      2^2048-9443
      2^2048-9509
      2^2048-11339
      2^2048-11837
      2^2048-12459
      2^2048-12855
      2^2048-13407
      2^2048-14505
      2^2048-15155
      2^2048-16773
      2^2048-18819
      2^2048-19575

      2^4096-2549
      2^4096-8067
      2^4096-8627
      2^4096-8799
      2^4096-9443
      2^4096-14477
      2^4096-16859
      2^4096-17555
      2^4096-18365
      2^4096-20655

      2^4096+1761
      2^4096+7227
      2^4096+7423
      2^4096+10093
      2^4096+10473
      2^4096+13965
      2^4096+17335
      2^4096+17355
      2^4096+19891
      2^4096+22803

      2^8192+897
      2^8192+9543
      2^8192+10813
      2^8192+13371
      2^8192+14931
      2^8192+14985
      2^8192+15505
      2^8192+15763
      2^8192+16305
      2^8192+19423

      2^8192-2439
      2^8192-5619
      2^8192-9345
      2^8192-9515
      2^8192-19085
      2^8192-19733
      2^8192-21713
      Tested up to 2^8192-43073, but I am out of time and have to go.

      Options for CPAPSieve would be:

      cpapsieve -b=2 -n=16384 -K=-1 -k=-250000 -O=14m -L
      cpapsieve -b=2 -n=16384 -k=1 -K=250000 -O=14p -L

      then do reverse 14m.in to get the minuses into n-1 to n-250000 order

      then use WinPFGW to test 14p.in and 14m.in files until enough PRPs
      are found. A range of 250000 should be enough for 2^(2^14)+-k range.
      This size would need increased as the size of the numbers increased
      (or if searching for more PRP's)
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