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Re: [PrimeNumbers] Re: k.2^n+/-1 series

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  • Barbara and Joe
    A belated reply here, but check my webpage www.glasgowg43.freeserve.co.uk/nashprim.htm for straightforwardly-generated numbers with very high Proth weight - in
    Message 1 of 12 , May 3, 2002
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      A belated reply here, but check my webpage www.glasgowg43.freeserve.co.uk/nashprim.htm
      for straightforwardly-generated numbers with very high Proth weight - in the equivalent context of Nash weight.

      In terms of searching through those in the webage, some of the k-values are already taken, including:

      986963835
      302627325
      302442855
      806586495

      (the last by me). There will be plenty of others available which should provide large numbers of small primes of the form k*2^n+1.

      If you want to know more about the divisibility properties of these numbers, then go to
      www.glasgowg43.freeserve.co.uk/pfaq6.htm

      Joe.

      -----Original Message-----
      From: robert44444uk <100620.2351@...>
      To: primenumbers@yahoogroups.com <primenumbers@yahoogroups.com>
      Date: 08 April 2002 02:33
      Subject: [PrimeNumbers] Re: k.2^n+/-1 series


      On the question of proth weights for k, the highest I found to date
      is for 39.37#+2.31#+20.29# (289939302102450) which has a weight of
      4.216. I'm sure there are higher values than this.

      I am not 100% convinced by the proth weight concept. I ran this
      number up to n= circa 3,200 both plus and minus one, and got 43 and
      31 primes, which seems pretty average to me. As a comparison,
      67#.2^n+1 plus yielded 70 primes up to n=3,300, (and 88 up to
      n=18,000) with a proth weight of (only) 4.191

      That said, Jack's applet is an interesting tool and I use it!

      Carlos Rivera has rejected 23#.2^n-1 as the most populous -1 series,
      (95 primes) because it has an index p/ln(n) of 8.00, compared to
      Jack's record of 9.083. It seems you must beat not only the absolute
      number of primes, but also the index to get a listing for puzzle 6
      (see http://www.primepuzzles.net/puzzles/puzz_006.htm)

      On processing speed - on my machine, PRP and pfgw are about the same.

      Regards

      Robert Smith




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