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Proth coefficients & weights

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  • jack@babybean.com
    ... Thank you for the congrats, Pavlos. Indeed, of the seven PCs available to me, three of them are spending all of their idle time looking for primes of the
    Message 1 of 2 , Feb 19, 2001
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      --- In primenumbers@y..., "Pavlos S." <pavlos119@y...> wrote:

      > Congratulations to g42 for the new and amazing prime:
      > 577294575*2^223519+1.It seems that this specific k
      > produces a great many primes.And also g42 has been
      > patient enough to seek in higher limits!Can anyone
      > tell me what the probability is that a
      > 10-million-digit prime of the form 577294575*2^n+1
      > exists that can be discovered by proth(i.e
      > 33219000<n<33554000)?

      Thank you for the congrats, Pavlos. Indeed, of the seven PCs
      available to me, three of them are spending all of their idle
      time looking for primes of the form 577294575*2^n+1.

      On your other question, my quick calculations give about a 10%
      probability that a prime of the form 577294575*2^n+1 would be
      found with 33219000<n<33554000.

      Just to discourage you from even trying, let me give you some
      raw numbers. I'm currently (in the n ~ 225000 range) expecting
      to find a new prime roughly every 100 CPU days. The amount of
      time expected to find primes is generally O(log(N)^3) -- see
      the explanation of production scores at:

      http://www.utm.edu/research/primes/bios/TopCodes.html

      A quick calculation shows that log(N) for your range is about
      150 times greater than log(N) for my range, so primes will take
      about 150^3 times longer to find... you'll expect to find a
      new prime roughly every 100*150^3 CPU days -- once every million
      CPU years!

      Given the number of tractable problems in computational math,
      it would be a shame to waste CPU cycles on such an impossible
      long shot. Offer some help with the Cunningham table projects,
      or finish computing the aliquot sequence starting at 276, or
      look for a Cunningham chain of length 20; you might even try
      to find an odd perfect number, or raise the lower bound for such
      numbers -- in my opinion, the discoverer of the first odd
      perfect number (if one exists) will be more famous than any
      discoverer of primes. But, that's just my opinion.

      Jack Brennen
      "g42"
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