It's the cataloging system used by Krause and Mishler (KM) for coins from a given country. They are listed in the Krause prices guides such as Standard World Coins 1901 to 2006.
As far as I know there is no master list of KM#'s as unto themselves they are not unique. You can have several different coins and each can have a KM#1 designation. What does make it unique is when you add the country name to it, United States KM#1, Ghana KM#1, etc...
If you are curious as to how the number system works it's really quite simple. You start off with a country or political state and their first year of coinage and the number begins from the lowest denomination to the largest based on a coin type and new numbers are added sequentially each year a new coin type is issued.
Let's use a modern version of this with Botswana. Botswana's first year of coinage was 1966 and they issued the following coins from lowest to highest: 50 cents & 10 thebe. This makes them KM#1 50 cents and KM#2 10 thebe. In 1976, new coin types were issued as follows: 1 thebe, 5 thebe, 10 thebe, 25 thebe, 50 thebe, 1 pula and 5 pula. So the new KM#'s became KM#3 1 thebe, KM#4 5 thebe, KM#5 10 thebe, KM#6 25 thebe, KM#7 50 thebe, KM#8 1 pula, and KM#9 5 pula.
If two varieties of a same coin type were issued then the number system changes by designating the varieties with a decimal point. If you look back at the Botswana example, we have a 1976 KM#4 5 thebe coin. As it turns out, those coins were issued with a reeded edge and plain edge (two varieties of the same coin type). To differentiate these, a decimal system is used so now we have a KM#4.1 5 thebe reeded and a KM#4.2 5 thebe plain.
Recording the KM# on your 2x2 is not a bad idea. KM#'s and Krause catalogs are one of the key reference points for world coin collectors.
Here is a good site that has quite a few modern KM#'s that may help http://(131231) Not Allowed - Auto-Removed /
If buying a price guide sounds like an unpleasant alternative then look in your local library one or buy an older used guide from Amazon
, E-bay, B&N for a few $$.