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idea for finding great mersenne primes

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  • Norman Luhn
    One year ago i had a found that 2^p-1 is prime when (x^(2^p-2)/p)=2^z mod 2^p-1. For all x, spezial x 2^k Example.p=17 2^17-1 is prime, because 19^7710=2^12
    Message 1 of 1 , Dec 31, 2001
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      One year ago i had a found that 2^p-1
      is prime when (x^(2^p-2)/p)=2^z mod 2^p-1.
      For all x, spezial x<>2^k
      Example.p=17 2^17-1 is prime, because 19^7710=2^12
      mod 2^17-1. The result is ever a power of 2,when 2^p-1
      a prime.

      When we find a number x und small exponent y
      and ABS(x^y-(2^p-1))=2^m Then can we easy check
      x^((2^p-2)/p)=2^m mod 2^p-1

      The smallest example is.
      prime 2^7-1.
      We take x=5 and y=3 , we get ABS(5^3-(2^7-1))=2
      -> 5^18=2^m mod (2^7-1), 5^3=-2 mod 2^7-1
      -> (-2)^6 is a power of 2 mod 2^7-1.
      (
      The smallest example is 2^5-1
      We test 3^6=14 mod 31. 3^3=-4 mod 31. (-4)^2=16 mod 31
      )

      This examples very rare, but when we find easy another
      example x^y-(2^p-1)=2^k then we have found a new
      mersenne prime 2^p-1





      best

      Norman








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