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Re: [PrimeNumbers] Twin primes' rule

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  • mikeoakes2@aol.com
    In a message dated 27/03/2001 15:12:06 GMT Daylight Time, ... I have checked the only if part of your iff rule with a short program. If (n,n+2) is a prime
    Message 1 of 2 , Mar 29, 2001
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      In a message dated 27/03/2001 15:12:06 GMT Daylight Time,
      torasso.flavio@... writes:
      > I found the following rule concerning twin primes:
      > n and n+2 are both prime iff
      > 2 [(n-1)/2]!^2 = \pm (5n+2) mod n(n+2)
      > the sign being "+" when n=4k-1, "-" when n=4k+1.
      >
      > Is it an interesting or trivial result?
      > Are there similar congruences for other prime pairs?
      >
      > Thanks for any comments

      I have checked the "only if" part of your iff rule with a short program.
      If (n,n+2) is a prime pair, then your equality mod n(n+2) is satisfied for
      the 17 prime pairs from (3,5) up to (239,241).
      It fails for (269,271) and (281,283).
      It is ok for (311,313) and (347,349).
      It fails for (419,421).
      It is ok for (431,433) and (461,463).
      It fails for all the remaining 633 primes pairs up to (46307,46309), which
      was the program's limit.

      Curious.

      Mike Oakes
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