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Re: [PrimeNumbers] Re: Goldbach conjecture

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  • Andy Swallow
    ... There were no grounds for believing that Li(n) would always be greater, the problem was that nobody could find a value for which pi(n) became greater,
    Message 1 of 11 , Sep 16, 2003
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      > There comes a point at least for me, when that data is entirely
      > convincing. I haven't looked at the relationship between pi(n) and Li
      > (n) , but was there was *really* convincing grounds to believe Li(n)
      > would always remain greater than pi(n) ?

      There were no grounds for believing that Li(n) would always be greater,
      the problem was that nobody could find a value for which pi(n) became
      greater, until Littlewood managed to show the existence of such a point.
      [In fact Littlewood showed that pi(n)>Li(n) infinitely often, and also
      Li(n)>pi(n) infinitely often.]
      I might add that this was purely an existence result, the constant in
      question being ineffective, i.e. couldn't be calculated. It was many
      years before a value, Skewes number, was placed on it.

      Andy
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