I've got a question.
Are we sure that the numbers are 100% random? I mean can there be a way of predicting exactly what the next key is or just it's range of values?
Yes. The numbers are 100% random.
This knowledge comes directly from the creator.
Does that mean that even predicting the region in 2^n is considered luck or is there a pattern in region changes?
This is known ... Each subsequent address is in the range of one higher than the previous one, i.e. if address #58 was in 2 ^ 57 then #59 is in 2 ^ 58.
2^n-1
n = number of wallet in this puzzles. (now the lowest prize is in #62)
This is the only rule that takes place here and also comes from the creator.