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17299Re: Prime certifacate / Pocklington test

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  • bhelmes_1
    Dec 9, 2005
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      --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@y...>
      wrote:
      >
      > From: "bhelmes_1" <bhelmes@g...>
      > > A beautifull evening,
      >
      > -6 C, 3pm, and the sun's already set. Beautiful indeed!

      The time depends on the country where you live.
      If you want to be accurate you can calculate where i would like to
      spend my holidays. :-)


      > > is the following prime number certificate correct.
      > > I used the test of pocklington for a certain kind of prime
      numbers.

      > I've not checked that your divisors are in fact divisors, I'll
      take that as
      > read. However, one thing that is technically part of the
      pocklington proof is
      > the number, a, such that a^((p-1)/d) == r where r is your d-th
      root, as given
      > above. The d-th root part is less important than the ((p-1)/d)-th
      root part,
      > i.e. a is more important than r. a is also usually a very small
      number, and
      > often the same for many d, so a is more convenient for keeping
      certificates
      > small too.

      I thought you can prove faster the certificate, if you give the d-th
      roots. If the prime number is greater than 10.000 digits, then you
      need a little time for calculating the roots.

      I do not know what kind of certifcate is usual. Is it enough to
      write down the divisors and an a (than the certificate is very short)
      or do you appreciate a little more text like above.

      Besides, I need 100 tests for a succesfull 1000 digit prime test.
      Is this a good or bad result for searching big primes ?

      Nice greetings from the primes
      Bernhard
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