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p-1 and p+1 test for primes

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  • bhelmes_1
    Dear David, this is more a mathematical question, i thought about: a) w1 | p-1 ; w1 2 there is a (non trivial) w1.th root of 1 b) jacobi (a, p)=-1 w2 | p+1 ;
    Message 1 of 1 , Jan 18, 2011
      Dear David,

      this is more a mathematical question, i thought about:

      a) w1 | p-1 ; w1>2
      there is a (non trivial) w1.th root of 1

      b)
      jacobi (a, p)=-1
      w2 | p+1 ; w2>2
      there is a (non trivial) w2.th root of 1 in the quadratic field of
      the adjoined square of a

      if a) and b) is right, p is prime

      There is an explication of the algorithm in Mupad:
      http://109.91.184.78/devalco/suff_2.html

      I tested some Carmichael Numbers but i did not found a counterexample.
      If you need a nice challenge, try to find one counterexample :-)

      Nice Greetings from the primes
      Bernhard

      http://devalco.de
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