Again, you are using the words "occur in sequence" which is not the same as "occur in a sequence". There's nothing in that book about this.
You're still assuming the probability changes just because you move from one key to the next. But there's no external entity that would do that (except faith maybe).
As I told you previously, you never want to lose your argument and you will always find a explanation that fits with what you preach. And I am the one quoting thinks while you only preach your words as true. It's great you read the book in less than 24 hours. However, when talking about events that 'occur in sequence', I mean that the events appear one after the other in a specific order. It doesn't necessarily mean that one depends on the other, but rather that there is an order. This is a typical fallacy in debates. You dismiss opposing ideas in a disparaging way to validate your point by saying things like 'except faith maybe'.
"
A compound event is also the outcome of an experiment, but can be broken down into a combination of simple events occurring simultaneously or in succession."
https://study.com/academy/lesson/compound-event-in-math-definition-example.htmlhttps://thirdspacelearning.com/gcse-maths/probability/combined-events-probability/#:~:text=Combined%20events%20in%20probability%20are,use%20the%20AND%20probability%20rule.
https://www.youtube.com/watch?v=EHU6pVSczb4If we want to find a RIPEMD-160 hash with 4 initial prefixes, for example:
123aThe probability of each independent character is 1/16 (since a hex has exactly 16 alphanumeric characters 0-9 a-f). So, the probability of the complete prefix
123a would be:
1/16 x 1/16 x 1/16 x 1/16 = 1/65.536.
And that's just the calculation for a 4-digit prefix. With 2 prefixes, it increases much more, and if you look for longer prefixes, it becomes even less probable.
Therefore, due to the uniform distribution of hashes, it is less likely that we will find a prefix close to another one.
A probabilistic software using a previous prefix as a reference point, where you skip millions of keys and where a coincidence or collision is less likely, is not a waste of time as you suggest. Instead, it would be another probabilistic option. In this case, where sequential brute force is exponentially demanding, a probabilistic search suggests a better strategy.
However, it is clear that you can skip the address, but it is less probable if you do the calculations correctly, adding a margin of error.