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running averages and gaps

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  • John W. Nicholson
    In the stock market, they have what is called a running average. I am wondering if anyone has done similar, but using a few twist. Instead of averages it
    Message 1 of 1 , Dec 10, 2004
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      In the stock market, they have what is called a running average. I
      am wondering if anyone has done similar, but using a few twist.
      Instead of averages it being the distance for pi(x2) – pi(x1) = dn
      (the gap)?

      This does not have to be limited to one prime, it can use a sum of
      gaps too.

      Another thought:

      A prime gap >= 2 is composed of composite numbers (CN) between two
      primes (p) and (q).
      1. There exist a prime factor (pf) for each CN which is < sqrt(q).
      2. The CN with the largest pf in the gap can be called a gap
      summate. On each side of a gap summate is a subgap.
      3. At least one subgap size is <= 1/2 of the total gap.
      ( A maximal gap will not double in size with the next maximal.)
      4. There is only one summate per maximal gap.
      5. There are two types of maximal gap primes, one in which the
      summate is the largest prime < sqrt (q), a progressive prime. The
      other type is regressive prime, a smaller prime < sqrt (q) is used
      as a summate.
      6. For q > 10000, sqrt(q) increases faster than 2*(q-p). This leads
      to regressive primes maximals. This comes from looking at the
      maximal data on http://www.trnicely.net/gaps/gaplist.html up to the
      40th * on the list and the above thoughts.

      Are these theorems?

      John
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