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Re: Interesting Pattern

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  • d.broadhurst@open.ac.uk
    Milton Brown wrote ... The latter is ID Number: A001562 (Formerly M3767 and N1537) Sequence: 5,7,19,31,53,67,293,641,2137,3011 Name: (10^p + 1)/11 is
    Message 1 of 6 , Aug 3, 2001
      Milton Brown wrote

      > 9901 (9909901,...) and 9091 (90901,...)
      > which also quite often are prime. I think David
      > indicated where these have been studied before.

      The latter is

      ID Number: A001562 (Formerly M3767 and N1537)
      Sequence: 5,7,19,31,53,67,293,641,2137,3011
      Name: (10^p + 1)/11 is prime.
      References J. Brillhart et al., Factorizations of b^n +- 1.

      in the EIS. But the former does not figure in the
      Cunningham project tables for cyclotomic
      factors of 10^n +/- 1.

      Perhaps you meant

      f(n)=(10^(6*n)+1)/(10^(2*n)+1)

      f(1)= 9901 is prime
      f(2)= 99990001 is prime
      f(3)= 999999000001 is prime
      f(4)= 9999999900000001 is prime

      Puzzle: Find the next prime of this form :-)

      David
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