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Re: Consecutive occurrences of decadal prime triplets

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  • rupert.wood@xtra.co.nz
    ... Thanks for that! Just to avoid unnecessary effort and extra computer time, are there any coding shortcuts for this kind of searching? Even in the 4-triplet
    Message 1 of 7 , Jan 1, 2010
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      --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
      >
      > I wrote:
      > > 9100524636850 + n, for n =
      > > 1, 7, 9, 31, 33, 37, 61, 63, 69, 91, 93, 99, 121, 127, 129.
      > >
      > > 283955584598830 + n, for n =
      > > 1, 7, 9, 33, 37, 39, 61, 63, 69, 91, 93, 97, 121, 123, 127.
      > >
      > > 488187768695650 + n, for n =
      > > 1, 7, 9, 31, 37, 39, 63, 67, 69, 93, 97, 99, 121, 127, 129.
      >
      > My search says these are the first three instances of 5 triplets.
      > I don't have resources to search for 6 triplets.
      >
      > --
      > Jens Kruse Andersen
      >

      Thanks for that!

      Just to avoid unnecessary effort and extra computer time, are there any coding shortcuts for this kind of searching? Even in the 4-triplet case there would be quite a bit of tedious checking to do in each iteration (just asking in case someone has developed some generic sort of prime pattern searching routine).
    • Jens Kruse Andersen
      ... I used my own unpublished prime pattern finder. It is modified for each search and not suited for sharing. It could probably easily find thousands of
      Message 2 of 7 , Jan 2, 2010
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        rupert.wood wrote:
        > Just to avoid unnecessary effort and extra computer time,
        > are there any coding shortcuts for this kind of searching?
        > Even in the 4-triplet case there would be quite a bit of
        > tedious checking to do in each iteration (just asking in
        > case someone has developed some generic sort of prime
        > pattern searching routine).

        I used my own unpublished prime pattern finder. It is modified for
        each search and not suited for sharing. It could probably easily
        find thousands of 4-triplet cases if it was modified for the purpose.

        There are many possible shortcuts evolving around avoiding or quickly
        eliminating cases where at least one number has a small prime factor.
        I searched each of the 194 admissible 5-triplet patterns one at a time,
        so in each case there were 15 numbers that had to be prime. Searching
        some patterns with few differences at the same time might be more
        efficient but I didn't have suitable code for that.

        A shortcut you may already use is to only make prp (probable prime)
        tests at first, and only make primality proofs later when there is a
        complete prp solution.

        Using fast tools like C instead of PARI/GP can also speed up many things.

        Robin Garcia wrote:
        > Does it not matter that primes exist between them?
        > For instance 9100524636850+n is also prime for n=21

        I listed this and the primes for the other cases in my first post
        http://tech.groups.yahoo.com/group/primenumbers/message/21242

        The original post said prime quadruplets are permitted and also listed:

        > There is an instance of 4 consecutive triplets at
        >
        > 5413 5417 5419; 5441 5443 5449; 5471 5477 5479; 5501 5503 5507.

        5431, 5437 and 5483 are also prime.

        --
        Jens Kruse Andersen
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