Late December 2007, I came across the following open problem

http://garden.irmacs.sfu.ca/?q=op/does_every_odd_number_coprime_to_its_euler_totient_divides_some_carmichael_number

I had done some earlier work on a related problem and adapted those methods to quickly find solutions to the computational challenge (finding Carmichael numbers that are multiples of 885, 2391, 2517, 2571, 2589, 2595, 2685, 2949).

This was to complete a list that Dr. Gerard P. Michon worked on. After sending those solutions in and corresponding with Gerard and Max Alekseyev through email, we extended the list from 3000-10000 in a short time.

http://home.att.net/~numericana/data/crump.htm

Gerard did the first pass through the list eliminating all the entries where no solution was found with 17 digits or less. I then followed up to fill in the gaps.

I used Visual C++ and the GMP arithmetic library for the programming. You can get one of the programs I wrote for this here:

http://immortaltheory.com/NumberTheory/gmp_michon.zip

It was used primarily for all the 3000-10000 multiples, with the exception of 8805 (it was found with a later program using a different method)

## Wednesday, January 2, 2008

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Note: The following address referred to in this post

http://home.att.net/~numericana/

is now

http://www.numericana.com/

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