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RE Prime gap merit record 34.98 by Herzog & Silva

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  • Jose Ramón Brox
    ... From: Mark Underwood The largest gap possible is apparently (I forgot where I read this) the square of the expected gap.
    Message 1 of 1 , Dec 7, 2005
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      ----- Original Message -----
      From: "Mark Underwood" <mark.underwood@...>

      The largest gap possible is apparently (I forgot where I read this)
      the square of the expected gap. The square of 41.23 is about 1700,
      and so 1442 is safely within the bounds. The universe is saved from
      primal unruliness yet again.

      --------------------------------------------------------------------

      Well, I think that what is conjectured is that the gap for p_n is bounded by M times (ln
      n)^2, where M is an undetermined constant ( If I remember correctly, in big o notation it
      reads p_n = O(ln^2 n) )

      http://mathworld.wolfram.com/Cramer-GranvilleConjecture.html

      I also think to have read that if RH is true, then M = 1. Not very truthful info, though.

      Regards. Jose Brox
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