Quote from: zielar on December 25, 2019, 12:06:04 PM

Hello,
I have a question to dispel doubts about the diff index in VanitySearch.
Suppose I am looking for the prefix "1RoseCross".
VanitySearch reports difficulty 173346595075428800 for the indicated prefix.

1. Is this value simply speaking - a group that creates 100% addresses where one of them will start with a given search (1RoseCross)?

Quote from: Jean_Luc on December 26, 2019, 10:09:52 AM

The difficulty is the search space size.
A difficulty of 173346595075428800 means that you have a probability of 1/173346595075428800 to find the result after 1 try.
After n tries, you can compute the probability to reach the desired address by using Bernoulli.
P(n) = 1-(1-1/173346595075428800)^n

To be more precise:

difficulty = 173346595075428800 means that:
--> there is a correct address each 173346595075428800 addresses
--> you have a probability of 1/173346595075428800 to find the result each 1 try
--> on average it takes 173346595075428800 tries to get 1 match (on average means: if you try many times 173346595075428800 tries), but if you do 173346595075428800 tries only once you will have only a 63% chance to get a match! No 100%!

Any vanitygen-like program computes right the probability to find a match in the particular sequence you are running, it doesn't compute anything "on average".

Search space size is not 173346595075428800, sometimes you have to generate more than 173346595075428800 addresses to get a match.
A group that creates 100% addresses where one of them will start with a given prefix has size 2^160 - 173346595075428800 + 1 (and I'm not considering the fact that there are 2^96 different private keys - means tries - for the same address).

Here more details:
https://bitcointalk.org/index.php?topic=5068417.msg48056010#msg48056010