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21249Re: [PrimeNumbers] Re: Consecutive occurrences of decadal prime triplets

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  • Jens Kruse Andersen
    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      I used my own unpublished prime pattern finder.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

      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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