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Re: [PrimeNumbers] Prime Gaps (Was "Prime gaps of 364,188")

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  • Jens Kruse Andersen
    ... The two last merits are below Nyman s lucky 32.28 which was record for 6 years. I haven t checked the rest. ... The Prime Pages has heuristic-based
    Message 1 of 1 , Dec 31, 2005
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      Jose Ramón Brox wrote:

      > >http://www.trnicely.net/gaps/gaplist.html
      >
      > Well, then what I was asking for, the smallest primes with biggest merit,
      > is a subset of that list:
      >
      > 2 -->1.44
      ...
      > 1693182318746371 --> 32.28
      > 55350776431903243 --> 31.07
      > 80873624627234849 --> 31.34

      The two last merits are below Nyman's lucky 32.28 which was record
      for 6 years. I haven't checked the rest.

      > Are there any heuristics to predict the size of the next merit and prime?

      The Prime Pages has heuristic-based conjectures about large prime gaps:
      http://primes.utm.edu/notes/gaps.html
      It doesn't mention merit directly but can be translated to merits.
      It says that in 1931 Westzynthius proved there are arbitrarily large merits.

      > Are there upper bounds that can never be trespassed, for a given size?

      Bertrand's postulate (proved by Chebyshev) says there is a prime between
      n and 2n.
      This gives a weak upper bound on merits for primes below a given size.

      --
      Jens Kruse Andersen
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