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Generalised Bi Triplets

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  • garychaffey2
    Bi twins are primes of the form N+/-1 and 2N+/-1. This idea cannot be extended to Triplets (i.e. N-1, N+1, N+5, 2N-1, 2N+1, 2N+5) since one of these six primes
    Message 1 of 1 , Jun 29, 2004
      Bi twins are primes of the form N+/-1 and 2N+/-1.
      This idea cannot be extended to Triplets (i.e. N-1, N+1, N+5, 2N-1,
      2N+1, 2N+5)
      since one of these six primes is always composite.
      However if we look at Generalised bi twins i.e. N+/-1 and bN+/-1 this
      can then be extended to Triplets
      As a small example (with b=4)
      2329017*4^5-1
      2329017*4^5+1
      2329017*4^5+5
      2329017*4^6-1
      2329017*4^6+1
      2329017*4^6+5
      Has anybody else looked at these before?
      Also can this idea be extended to n-tuplets of arbitrary length? I
      have a hunch that it can but would be interested to see a proof or
      counter example...

      Gary
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