The calculation of possible numbers is much more complicated. the equasion 37^63 does not correctly calculate it either but is a fairly good ballpark figure. When using a-z,0-9, plus hyphen, there are 37 possible standard characters. However, a domain can't start or end with a hyphen, and can't have two hyphens together in the 3rd and 4th position which indicates an IDN name. The 37^63 also assumes that ALL domains ARE 63 characters, which most are not. Therefore, I believe, the number to multiply is 38 with the 38th character being the possibility of no character or a shorter domain. You would also have to consider that 1 and two letter domains are not possible in most TLD's, and some that exist are grandfathered in. A few domains have others that can't be registered since their are reseved names, masks such as .us that does not allow registering strings that look like zip codes or phone numbers and domains higher than 5 digits. You would have to do a calculation based on each individual TLD's rules for reserved names and length restrictions.