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24863Re: [PrimeNumbers] Quadruplets 90 apart with intermediate decadal triplets

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  • Jens Kruse Andersen
    Feb 11, 2013
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      woodhodgson wrote:
      > The set {11,13,17,19, 41,43,47, 71,73,79, 101,103,107,109}
      > shows two sets of quadruplets 90 apart, and the intervening
      > "+30" and "+60" decades have triplets (in the decadal sense
      > that I use the term, not necessarily ones with a minimal
      > span of 6).
      >
      > Does anyone have a list of the next few occurrences of this pattern?

      There are only 2 admissible patterns, the above and its mirror
      {11,13,17,19, 41,47,49, 73,77,79, 101,103,107,109}

      A search found 10 occurrences in total below 10^17.
      2 of them are the mirror pattern.
      The first prime and the number of other primes in the interval:

      11, 11 other primes
      549758002658141, 2 other primes
      1444747726722731, 1 other prime
      4869691549793501, 2 other primes
      7973040075706331 (mirror pattern), 1 other prime
      21603285535472981, 0 other primes
      21859392938284241, 1 other prime
      23490659029317911, 0 other primes
      28423532235584111 (mirror pattern), 1 other prime
      94859808174585731, 0 other primes


      The first case of 4 prime quadruplets as closely together as admissible is in
      http://tech.groups.yahoo.com/group/primenumbers/message/18318:
      300000224101777931 + n,
      for n in {0,2,6,8, 90,92,96,98, 180,182,186,188, 210,212,216,218}

      --
      Jens Kruse Andersen
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