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sufficent proof for primes ?

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  • bhelmes_1
    A beautifull evening I have tried to make a sufficent proof for all odd primes: http://beablue.selfip.net/devalco/suf_prime.html There remains two question: 1.
    Message 1 of 50 , Aug 5, 2010
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      A beautifull evening

      I have tried to make a sufficent proof for all odd primes:
      http://beablue.selfip.net/devalco/suf_prime.html

      There remains two question:
      1. if (1+sqrt (a))^d mod p is a natural number,
      does this reveal a group with order d in the ring of natural numbers with an adjoined square ?

      2. if p=f*g and there exist a group in p with order d in the ring of natural numbers with an adjoined square,
      does that means, that f and g have also a group with order d.

      The test bases on the symmetry of primes shown by
      http://beablue.selfip.net/devalco/symmetrie_adjoined.htm

      I hope that there are some people who are interested in the proof
      and who can help me to finish the proof.

      The best greetings from the primes
      Bernhard

      http://devalco.de
    • djbroadhurst
      ... [4] is meaningless, as it stands. You should write a double mod: 4. (1+x)^p = 1-x mod(x^2-a,p) ... There is no reason whatsoever to believe that [1] to [4]
      Message 50 of 50 , Sep 29, 2011
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        --- In primenumbers@yahoogroups.com,
        "bhelmes_1" <bhelmes@...> wrote:

        > 1. let a jacobi (a, p)=-1
        > 2. let a^(p-1)/2 = -1 mod p
        > 3. a^6 =/= 1 mod p
        > 4. (1+sqrt (a))^p = 1-sqrt (a)

        [4] is meaningless, as it stands.
        You should write a double mod:

        4. (1+x)^p = 1-x mod(x^2-a,p)

        > 1. Is it possible that there are other exceptions

        There is no reason whatsoever to believe that
        [1] to [4] establish that p is prime. Morevoer,
        some folk believe that, for every epsilon > 0,
        the number of pseudoprimes less than x may
        exceed x^(1-epsilon), for /sufficiently/ large x.

        > 2....
        > there is a cyclic order ...

        > 3....
        > there is a cyclic order ...

        The group of units (Z/nZ)* is /not/ cyclic
        if n has at least two distinct odd prime fators.

        David
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