So if someone was to "steal" my card that was for example

3760 123 456 71000

and I were to report it to amex, the person who stole my card should know that my new card number is:

3760 123 456 7200X

With X being a check digit that they could get off the internet or work out VERY quickly?

I know from past losses amex keep the same expiry date for "lost / stolen" cards so the thief would know the new card number and expiry date. It does not sound to secure to me