If the calculations and the data I researched are correct: its as hard to find a private key to a given address as its hard to find 0,01mm^3 of water in the pacific (!) ocean.
This is not correct.
There are 2
96 = 7.9*10
28 private keys for each address, but you don't know any of them.
If you had the list of those 7.9*10
28 private keys, it would be as difficult to find the particular private key that someone was using as it would be to find find 0,01mm^3 of water in the pacific ocean. However, if you had the list of those private keys, then you wouldn't need to find the particular private key that someone was using, because any and all of the keys that you have in that list would work just fine to sign the transaction.
The problem you'll run into it that there are nearly 2
256 possible private keys, and only 2
96 of them are useful if you are trying to find a private key to sign transactions that spend someone else's bitcoins. As such, the ratio you are working with is 2
96 / 2
256 which you'll find is one out of every 2
160 private keys that you check (which makes sense, since there are 2
160 possible addresses and you're looking for a private key to exactly one of them).
2
160 is approximately
1.5 * 1048As you pointed out:
We have 714* 10^6 * 10^12 (km^3 to liter) * 3*10^25 = 714*3 * 10^(6+12+25) = 2.142 * 10^43 water molecules.
As such, it IS easier to find a single molecule of water in the entire Pacific Ocean than it is to find someone's private key.
Try the math again, and I suspect you'll find that it is easier to find a single molecule of water on the entire earth (including buried deep underground, in the ice caps, or vapor in the atmosphere).
After that, try this math:
How many total molecules (water or otherwise) exist on the earth?