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carmichael numbers

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  • plano9
    Do all carmichael numbers contain -only- 3 factor pairs? I tested the carmichaels under 30,000 and all did, granted, that s only 10 numbers. Here s the
    Message 1 of 2 , Oct 9, 2004
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      Do all carmichael numbers contain -only- 3 factor pairs? I tested
      the carmichaels under 30,000 and all did, granted, that's only 10
      numbers.

      Here's the results-

      561: 3 , 187; 11 , 51; 17, 33
      1105: 5 , 221; 13 , 85 ; 17 , 65
      1729: 7 , 247; 13 , 133; 19 , 91
      2465: 5 , 493; 17 , 145; 29 , 85
      2821: 7 , 403; 13 , 217; 31 , 91
      6601: 7 , 943; 23 , 287; 41 , 161
      8911: 7 , 1273; 19 , 469; 67 , 133
      10585: 5 , 2117; 29 , 365; 73 , 145
      15841: 7 , 2263; 31 , 511; 73 , 217
      29341: 13 , 2257; 37 , 793; 61 , 481

      Plano9
    • Jens Kruse Andersen
      ... Under 30,000 is indeed a very short search for numbers with many factors. Why do so many people post trivial questions or wrong claims on mail lists
      Message 2 of 2 , Oct 9, 2004
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        plano9 wrote:

        > Do all carmichael numbers contain -only- 3 factor pairs? I tested
        > the carmichaels under 30,000 and all did, granted, that's only 10
        > numbers.

        Under 30,000 is indeed a very short search for numbers with many factors.
        Why do so many people post trivial questions or wrong claims on mail lists
        instead of doing a little computational or Internet research first?
        Maybe they are lazy and think trivial questions on mail lists _is_ proper
        Internet research?
        Maybe the best response would be to not answer?
        "I'm feeling lucky" for "carmichael numbers" at Google answers the question
        faster than it can be written and mailed:
        41041 = 7*11*13*41 is the first with 4 prime factors.

        The first Carmichael with n prime factors is in
        http://www.research.att.com/projects/OEIS?Anum=A006931

        Richard Pinch has continued to 34 prime factors:
        http://www.chalcedon.demon.co.uk/cartable.html#Smallest

        --
        Jens Kruse Andersen
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