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Quadruplets 90 apart with intermediate decadal triplets

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  • woodhodgson@xtra.co.nz
    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
    Message 1 of 3 , Feb 10, 2013
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      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?
    • Jens Kruse Andersen
      ... 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
      Message 2 of 3 , 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
      • woodhodgson@xtra.co.nz
        Thank you Jens, also to Maximilian for his replies. It certainly confirms a long gap to the next occurrences. No doubt these should occur infinitely often
        Message 3 of 3 , Feb 11, 2013
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          Thank you Jens, also to Maximilian for his replies. It certainly confirms a long gap to the next occurrences. No doubt these should occur infinitely often according to general conjectures.

          --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" wrote:
          >
          > 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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