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Re: [PrimeNumbers] Conjecture for primes

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  • Peter Kosinar
    ... Now, replace primes greater than 3 by integers congruent to +1 or -1 modulo 6 . Since any multiple of 6 behaves the same way on left-hand and right-hand
    Message 1 of 2 , Jul 28, 2012
      > If p and q are primes  and p and q >3 we have:
      >
      > Floor[(p+q)/6]=Ceiling[(Floor[p/3]+Floor[q/3])/2]

      Now, replace "primes greater than 3" by "integers congruent to +1 or -1
      modulo 6". Since any multiple of 6 behaves the same way on left-hand and
      right-hand side of the equality (and thus we can cancel it out), we only
      need to check three possible cases:

      Floor((1+1)/6) = Ceiling[(Floor(1/3)+Floor(1/3))/2],
      Floor((1+5)/6) = Ceiling[(Floor(1/3)+Floor(5/3))/2] and
      Floor((5+5)/6) = Ceiling[(Floor(5/3)+Floor(5/3))/2]

      Q.E.D.

      Peter

      [Non-text portions of this message have been removed]
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