16142Prime # Odometer (prime # wheel) & Carmichael #
- Feb 28, 2005Hello,
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).
360 degrees, back to TDC. Then rotate it again 360 degrees. Then add to this
another circle of 2 units circumference. Rotate the first circle again 360
circle is back to TDC, but #2 circle, which rotates like an odometer along with
#1, but 1/2 the distance, is off TDC. As only #1 circle is back to TDC after
degrees rotation, make another circle of 3 units circumference. Rotate #1 circle
degrees. Now #1 and #2 circles are at TDC, so don't add the #4 circle. Rotate #1
through to TDC and as only #1 is at TDC and #2 and #3 are off TDC, add another
this time of 5 units circumference. Continue adding circles of P units
when the #1 circle is at TDC and all other (prime #) circles are off TDC. You
generate all the primes.
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