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twin prim conjecture extended

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  • Sebastian Martin
    Hello I have extended the conjecture: p, q consecutive primes p
    Message 1 of 1 , Jul 6 4:30 PM
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      Hello



      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

      3) w=sqrt[p*q+1] is integer



      1 --> 2 is easy.

      2 -->3 ¿???



      3 --> 1 p*q+1=k^2 then p*q=k^2-1 and then
      p*q=(k+1)(k-1)
      and therefore q=k+1 and p=k-1 because p and q
      are prime numbers . Now becomes q=p+2

      Note: if p and q are consecutive primes and z, w are
      both integers we have z=w.

      Sincerely

      Sebastian Martin Ruiz





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