Assuming that the name of every power of 10 greater than    ends in "-illion" (like million, billion, trillion, etc.), then the iban numbers are finite. Counting 0 (zero) there are 30276 of them, the largest begin 777777.

Iban numbers belong to the same family of aban numbers, eban numbers, oban numbers, and uban numbers. All quite boring, if I may speak my mind...

As for the above sets, the definition is not really precise, since large numbers may have non-standard names.

The first iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many iban numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.