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Re: Quadruplets 90 apart with intermediate decadal triplets

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  • 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 1 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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