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Re: [PrimeNumbers] Chains of primes of length n

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  • Jens Kruse Andersen
    ... A set by definition relying on the number of primes or composites is questionable for The Largest Known Simultaneous Primes at
    Message 1 of 2 , Feb 2, 2005
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      Robin Garcia wrote:

      > Define a chain of primes of length n: {p_1,p_2...,p_n} such that
      > C(p_(k-1))=p_(k)+1 for all 2<=k<=n where C(p_(k-1)) is the p_(k-1)-th
      > composite.
      > Example: {197,251,317} is a chain of length 3 because C(197)=252=251+1
      > and C(251)=318

      > Yet another sets of simoultaneous primes,Jens.

      A set by definition relying on the number of primes or composites is
      questionable for The Largest Known Simultaneous Primes at
      http://hjem.get2net.dk/jka/math/simultprime.htm
      I might allow this case because it seems harder than other allowed forms. I
      wouldn't if it was easier.

      > Where (number of digits) do you think we would find a 19-chain and WHEN?

      I haven't estimated number of digits but it's probably large. And when?
      Long after other 19-sets have been found. I don't think a record of this form
      will ever make the list.
      The only practical algorithm seems to be exhaustive computation of all primes.
      Other forms can be sieved with faster methods.

      --
      Jens Kruse Andersen
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