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Re: [PrimeNumbers] Consecutive occurrences of decadal prime triplets

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  • Robin Garcia
    Does it not matter that primes exist between them? For instance 9100524636850+n is also prime for n=21 [Non-text portions of this message have been removed]
    Message 1 of 7 , Dec 31, 2009
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      Does it not matter that primes exist between them? For instance 9100524636850+n is also prime for n=21





      [Non-text portions of this message have been removed]
    • 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 2 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 I used my own unpublished prime pattern finder.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 3 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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