It isn't 0-9and a-z (36) but rather 0-9a-f (16) Ie. Hexadecimal.
Since it takes 2 hex digits to make a byte, and 17 digits isn't divisible by 2; the odds are that they are simply 64-bit (8-byte) integers, displayed in hex and with a single digit checksum.
And unsigned 64-bit integers gives 2^64 = 18,446,744,073,709,551,616; or ~18e18
Which is ten orders of magnitude less than your calculation, but still sufficient that every person on the planet could deploy 2.5 billion of each resource type and still leave change.
(An IT correspondent that doesn't recognise hex? )