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Re: [PrimeNumbers] Prime Number GAP of 123,380

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  • Jens Kruse Andersen
    ... The gap has merit 123380 / log(10^12002-17189) = 4.46. This means it is around 4.46 times larger than average for that prime size. Rough heuristics
    Message 1 of 2 , Dec 27, 2005
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      Milton Brown wrote:

      > Prime GAP of 123,380.
      > I have just submitted 10^12002+106191 as PRP.
      > This together with 10^12002-17189, previously submitted
      > yields the prime number gap.

      The gap has merit 123380 / log(10^12002-17189) = 4.46.
      This means it is around 4.46 times larger than average for that prime size.
      Rough heuristics indicate 1 in e^m random gaps have merit above m.

      Here are 176 larger gaps: http://www.trnicely.net/gaps/g100k.html
      They all have much better merits. Most are between 10 and 15, the best is
      18.33 (gap size 337446 with proven primes). That page accepts merits as low as
      Milton's, but it appears nobody has bothered to submit them.

      The Top-20 Prime Gaps are at
      http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm
      This includes the 2 Megagaps on http://www.trnicely.net/gaps/g1m.html

      --
      Jens Kruse Andersen
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