Here is a posting about Carmichael numbers that was sent to the number theory mailing list.
Andrew Granville has written extensively on Carmichael numbers, including a joint paper showing that there are infinitely many Carmichel numbers. You can find links to his work here. You will need a postscript reader to read them. (If you access them from an X-windows client on our unix cluster, a postscript reader will launch automatically if you click on the articles.)