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10695Re: [PrimeNumbers] Re: primes close to 2^(2^n) for n = 11..14

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  • Phil Carmody
    Jan 5, 2003
      --- "paulunderwooduk <paulunderwood@...>" <paulunderwood@...> wrote:
      > --- richard_heylen wrote:
      > > Judging from the conjectured density of primes in this region you
      > > were quite lucky!
      >
      > Nothing more than PNT and Poisson, with a touch of Irish blood.
      >
      > You can strengthen these numbers by running
      > />pfgw -tc PRPfile
      >
      > this will test for "Fermat and Lucas PRP".
      >
      > I don't know of any composites that pass this. Does anyone else know?

      25

      It's a 7-PSP and a LPSP(1,-1)

      If you're using the LPSP definition to include GCD(n,D)==1, as C&P do, then

      377 is a 12-PSP and a LPSP(1,-1)

      > If you wanted to be even more sure you could use "Perrin
      > pseudoprimality test" or one simmilar, but these are not part of PFGW.

      Simply using the strong version (the 1 must be preceded by a -1) of each PRP
      test you'll get rid of 95% of these jokers. There's very rarely a reason for
      running a weak test rather than a strong one.

      Phil


      =====
      The answer to life's mystery is simple and direct:
      Sex and death. -- Ian 'Lemmy' Kilminster

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