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Re: [PrimeNumbers] summing primes to yield new primes

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  • Phil Carmody
    ... You re permitted to start with 3s, so that can be extended by 2. 0,1,1 = 1,1,2 0,0,1 = 0,1,1 ... (2,2,6) doesn t exist, so (2,2,2) doesn t lead there. In
    Message 1 of 4 , Jun 19, 2012
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      --- On Tue, 6/19/12, Maximilian Hasler <maximilian.hasler@...> wrote:
      > b) if not, what's the maximum length, and why? What V_0 leads to the
      > > smallest final prime?

      > the maximum length is 4, as you can see when you look at the
      > sequence V_i
      > mod 3:
      > 1,1,1 => 1,1,0
      > 2,2,2 => 2,2,0
      > 1,1,2 => 1,2,1
      > 1,2,1 => 2,1,1
      > 2,1,1 => 1,1,1
      > 1,2,2 => 2,2,2
      > 2,1,2 => 1,2,2
      > 2,2,1 => 2,1,2

      You're permitted to start with 3s, so that can be extended by 2.
      0,1,1 => 1,1,2
      0,0,1 => 0,1,1

      > what is the "final prime" ?
      > (2,2,2) leads to (2,2,6), so the final prime is 2 ?

      (2,2,6) doesn't exist, so (2,2,2) doesn't lead there.

      In the <3,3,5> example I gave, 19 is the final prime, as no other primes were added after it.

      > >  2) As above, but with n=5
      > > 3) As above, but with n=7
      > > 4) Generalise, what do you predict for other n?
      > >
      > It seems that in these cases the maximum length is always
      > 5. But I may be wrong...

      So you don't think the 5-tuplet
      [5, 83, 3, 7, 3]
      would be extended in turn 8 times by the primes
      [101, 197, 311, 619, 1231, 2459, 4817, 9437]
      (and no, that's not the answer, merely illustrative)?

      It seems you've made some assumptions that have stopped you from investigating every possibility.

      Phil
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