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19668Re: Big PrimoProth prime number

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  • Robert
    Oct 29, 2008
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      --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
      <jens.k.a@...> wrote:
      >
      > I wrote:
      > > A Proth prime is k*2^n+1 with k < 2^n.
      > > A PrimoProth prime is based on this, a Proth prime where k is a
      primorial:
      > > m#*2^n+1 with m# < 2^n
      > > However, m#*2^n-1 with m# < 2^n also appears to be allowed.
      >
      > After looking at more Google hits, it actually appears that the few
      people
      > searching or listing PrimoProths use different definitions or don't
      state a
      > definition at all. This confusion may be caused by Henri Lifchitz who
      > introduced the concept but himself seems unclear with the definiton and
      > inconsistent in the alleged records, both regarding whether there is an
      > upper and a lower limit on m#.
      >
      > --
      > Jens Kruse Andersens
      >

      I was involved some years ago as a coordinator for primes of the
      series n#/2*2^n+/1, which I called primoproths, influenced by Henri
      -see http://home.btclick.com/rwsmith/pp/page1.htm

      As suspected the largest primes discovered involve k=3 and k=15. The
      Riesel series k=15 is being actively searched and is at n=1834000 see:
      http://www.mersenneforum.org/showthread.php?t=6338. k=3 search is well
      known.

      The attractions of primoproths were diminished when it was discovered
      that Payam numbers gave greater density of primes and active searching
      went into abeyance.

      But these are good finds, so congrats
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