The reason why I ask this question is because of the pattern I've seen with Japanese numbers. Once you have to repeat a number to describe itself, you get a new unit. For example, 十十 = 百, 百百 = 万, 万万 = 億. So it seems that 千 is a number that had some Western influence in its creation. Implying that it was a number that created in more recent times (ie. the last 200 to 300 years). Am I in the right direction with this pattern I'm seeing? Or is this just coincidence?
The Japanese number system (which I believe is derived from the Chinese one) is pretty similar to the western one (just to call it something), except it breaks at every 4 digits instead of every 3 digits.
0-9999 兆 0-9999 億 0-9999 万 0-9999
0-999 billion 0-999 million 0-999 thousand 0-999
(assuming you're from a part of the English speaking world which doesn't use milliards or "thousand million"s).
The confusing thing about the Japanese system, though, is that when written with digits, it still puts commas at every third digit. This is most likely from western influence.
Slightly off topic, but...
Your idea is interesting, since it would be theoretically possible to have a number system where digits break in a "binary" fashion:
0-99999999 億 0-9999 万 0-99 百 0-9 十 0-9
I don't know if any language breaks digits in this way, though.