Re: [Phys-l] Carmichael numbers agai

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

I don't think the original statement was ever meant to be a definition.
It was a necessary but not sufficient condition.

*All Carmichael numbers are the product of 3 or more primes, but not all
products of three or more primes are Carmichael numbers 

Just like

* All primes are odd, but not all odd numbers are prime.

Do a web search if you want a complete definition.  I tried but didn't
find it terribly enlightening.  Personally, they might be interesting in
Number Theory, I don't see that they have enough impact in science to
warrant much more discussion here...


Tim F

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John
Clement
Sent: Monday, May 21, 2007 8:05 AM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] Carmichael numbers agai

Then the definition as originally given is not complete.  If a
Carmichael
number is simply the product of 3 primes, then 2 should be included as a
prime.  Is there a minimum prime number allowed, of is 2 just excluded?

John M. Clement
Houston, TX

> This discussion has wandered off quite a bit from my original joke
about
> the
> military advantage of "superior numbers"!
>
> A quick summary: There are NO even Carmichael numbers.  All Carmichael
> numbers
> are odd.  Furthermore, they are all the product of three or more
distinct
> primes.  But, of course, few products of three or more distinct primes
are
> Carmichael numbers.
>
> Now, back to transplanting my summer squash.
>
> Laurent Hodges


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