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RE twin prim conjecture extended

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  • Jose Ramón Brox
    ... From: Sebastian Martin ... Counterexample [contraejemplo]: p = 3, q = 11 z = sqrt( (p^2+q^2)/2 -1 ) = = sqrt( (9+121)/2 -1 ) = =
    Message 1 of 2 , Jul 7, 2006
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      ----- Original Message -----
      From: "Sebastian Martin" <sebi_sebi@...>

      >I have extended the conjecture:
      >p, q consecutive primes p<q
      >are equivalents:
      >1) p q are twin primes
      >2) z=sqrt[(p^2+q^2)/2-1] is integer

      Counterexample [contraejemplo]:

      p = 3, q = 11

      z = sqrt( (p^2+q^2)/2 -1 ) =

      = sqrt( (9+121)/2 -1 ) =

      = sqrt( 130/2 -1 ) =

      = sqrt(64) = 8

      There are plenty more... [Hay muchos más...]
      (3,31), (7,59), (11,23), (11,41)...

      Dude, I thought you had done an extended search! :-( [Tío, ¡creía que habías hecho una
      búsqueda exhaustiva! :-(]

      Pari-GP code:
      forprime(p=3,100,forprime(q=3,100,if(issquare((p^2+q^2)/2-1),print(i","j)))

      3,5
      3,11
      3,31
      5,3
      5,7
      7,5
      7,59
      11,3
      11,13
      11,23
      11,41
      11,67
      13,11
      17,19
      19,17
      23,11
      29,31
      31,3
      31,29
      31,79
      31,97
      41,11
      41,43
      43,41
      59,7
      59,61
      59,83
      61,59
      67,11
      71,73
      73,71
      79,31
      83,59
      97,31

      Regards. Jose Brox
    • Jose Ramón Brox
      ... From: Jose Ramón Brox ... Ooops... as Paul Jobling noted to me, I missed the condition of p and q being _consecutive_. Sorry. Jose
      Message 2 of 2 , Jul 7, 2006
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        ----- Original Message -----
        From: "Jose Ramón Brox" <ambroxius@...>

        >Counterexample [contraejemplo]:
        >p = 3, q = 11
        >(...)

        Ooops... as Paul Jobling noted to me, I missed the condition of p and q being
        _consecutive_. Sorry.

        Jose Brox
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