Re: [Phys-l] Carmichael numbers agai

["Laurent Hodges" <lhodges@iastate.edu>]

> 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?  :-)

Laurent Hodges