I am confused. If all Carmichael numbers are the product of three primes and
2 is a prime number, it would seem that there is a large number of even
Carmichael numbers???
Too much of a good thing is wonderful!
From: "Laurent Hodges" <lhodges@iastate.edu>
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To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Subject: Re: [Phys-l] Carmichael numbers agai
Date: Thu, 17 May 2007 09:02:15 -0500 (CDT)
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FILETIME=[2A1C2740:01C7988C]
> Can you explain why I should be interested enough in Carmichael numbers
to
know off-hand what the smallest one is? Do they have applications in
physics?
Personally, I had never heard of them before :-)
Carmichael numbers are a nuisance. Because they exist, the converse of
Fermat's
Little Theorem is not true; if it were true, checking the primality of an
integer would be a pretty trivial matter. (Prime numbers do have some
uses.)
Knowing the Carmichael numbers is about as useful as knowing pi to 24,512
digits, or whatever the European record is. But if your empire's military
success depends on having "superior numbers," you want to know stuff like
this,
don't you think? :-)