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Re: Proof of D. Andrica conjecture.

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  • richard042
    ... Maybe, Bertrand/Tschebycheff: pn
    Message 1 of 2 , Aug 3, 2002
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      --- In primenumbers@y..., "John W. Nicholson" <johnw.nicholson@a...>
      >
      > Do y'all See any problems?

      Maybe,

      Bertrand/Tschebycheff: pn<(pn+1)<2*pn
      Take: sqrt(pn) < sqrt(pn+1) < sqrt(2*pn)
      divide by constant c: sqrt(pn)/c < sqrt(pn+1)/c < sqrt(2*pn)/c

      A.) subtract lhs: 0 < (sqrt(pn+1)-sqrt(pn))/c < (sqrt(2*pn)-sqrt
      (pn))/c

      Regardless of the value of c, A.) must hold.
      We need to get to Andrica's conjecture: sqrt(pn+1) - sqrt(pn)<1.
      So, multiply A.) by c to get:
      B.) 0 < sqrt(pn+1)-sqrt(pn) < sqrt(2*pn)-sqrt(pn)

      We can use B.) to prove Andrica's Conjecture only
      if it is always true that rhs <1 - i.e.:
      sqrt(2*pn)-sqrt(pn) < 1
      divide by c=sqrt(pn)to get:
      sqrt(2)-1 < 1/sqrt(pn)
      which is only true for n=1

      QESh..

      -Dick Boland
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