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Re: Prime Gap of 398,370

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  • Jens Kruse Andersen
    ... Congratulations! The merit of the gap is 398370 / log(10^14173-51197) = 12.21. After years with smaller merits, you finally got a large gap qualifying for
    Message 1 of 2 , Feb 23, 2007
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      February 17 Milton L. Brown wrote:
      > The following PRP's produce a prime number gap of 398,370
      >
      > 10^14173+347173
      > 10^14173-51197

      Congratulations!
      The merit of the gap is 398370 / log(10^14173-51197) = 12.21.
      After years with smaller merits, you finally got a large gap
      qualifying for http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm

      This is by far the largest gap with merit>10 and "basic" expression
      (short expression with +-*/^, but not !#).
      My old record from 2003 was a gap of 84630 after PRP3039 = 2^10093-
      80445, with merit 12.10.

      My rough heuristics say: The chance that the gap crossing a random
      number (10^n for integer n qualifies) has merit>12 is around 1 in
      e^12/12 = 1 in 13563. Most large gaps are found around non-random
      numbers.

      Thanks to Torbjörn Alm for verifying the gap with PrimeForm.

      --
      Jens Kruse Andersen
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