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15547Re: [PrimeNumbers] Extension of Cunningham chains

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  • mikeoakes2@aol.com
    Nov 13, 2004
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      Jack wrote:-
      >>Can anybody find any longer such chains each with an equal number
      >>of divisors, either with 4, 8, or some other number?

      I wrote:
      >With 3 divisors, each must be the square of a prime, of course.
      >Are there any such chains of length > 1? (I haven't searched.)

      In fact, there are chains of length 2, but no longer.
      [
      The first few are:-
      2^2, 3^2
      5^2, 7^2
      29^2, 41^2
      ]
      The proof is relatively straightforward.
      Anyone?

      -Mike Oakes


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