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Prime # Odometer (prime # wheel) & Carmichael #

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  • Bill Krys
    Hello, why would a prime # odometer (Brute Force Prime seive) not seive out Carmichael # s when it is composite. When the carmichael # had it s turn to come up
    Message 1 of 1 , Feb 28, 2005
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      Hello,

      why would a prime # odometer (Brute Force Prime seive) not seive out Carmichael #'s when
      it is composite. When the carmichael # had it's turn to come up for evaluation it would
      have the prime factors at TDC? For example, take the Carmichael number 561=11*17*3. When
      561 is evaluated, 1, 3, 11 & 17 are all TDC, so it would not be added as a prime to the
      prime # odometer.

      take a circle of 1 unit circumference, with a mark at top dead center (TDC).
      Rotate it
      360 degrees, back to TDC. Then rotate it again 360 degrees. Then add to this
      circle
      another circle of 2 units circumference. Rotate the first circle again 360
      degrees. #1
      circle is back to TDC, but #2 circle, which rotates like an odometer along with
      circle
      #1, but 1/2 the distance, is off TDC. As only #1 circle is back to TDC after
      another 360
      degrees rotation, make another circle of 3 units circumference. Rotate #1 circle
      360
      degrees. Now #1 and #2 circles are at TDC, so don't add the #4 circle. Rotate #1
      again
      through to TDC and as only #1 is at TDC and #2 and #3 are off TDC, add another
      circle,
      this time of 5 units circumference. Continue adding circles of P units
      circumference only
      when the #1 circle is at TDC and all other (prime #) circles are off TDC. You
      will
      generate all the primes.

      Bill


      =====
      Bill Krys
      Email: billkrys@...
      Phone: 780.474.9493
      Cell: (780) 995-6214
      ICQ: 122663993
      12112-50 Street
      Edmonton, Canada T5W 3C5



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