Quote from: HNajafi on Today at 08:32:00 AM

Is the possibility of discovering private keys with random testing by considering the increasing number of e-wallet?

Yes, there is a tiny tiny tiny possibility of generating private keys that were generated before. The chances are described on the above posts, the fact that there is 1 in x possibilities shouldn't trick you. We can't even pretend to understand how big is that number, it's above human's standards. It's never happened and I hope it'll never be.

Quote from: HNajafi on Today at 08:32:00 AM

what the prevention solution in cryptocurrency such as bitcoin is?

You can't prevent someone from calculating. Everyone's free to brute force bitcoin addresses.

Quote from: HNajafi on Today at 08:32:00 AM

Is there any mechanism such as "I am not a Robot" (Captcha) or blocking the user with the iterative wrong private key?

In order for this to happen Bitcoin addresses must be generated over a centralized authority that will filter users' private keys to prevent any collisions. I guess you understand that this is against decentralization, against its purpose.

I believe that you haven't been convinced that it's impossible to achieve such thing, so I'll tell you one last thing:
With the current difficulty, in order to mine a block, you'll have to try among ~23,100,000,000,000 * 2³² = ~99,213,744,537,600,000,000,000 combinations. If you'd be able to generate 1 hash, then you'd have 1 in that number, to be rewarded with 6.25 fresh bitcoins.

Compare these numbers:

99,213,744,537,600,000,000,000
1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976

Not to mention that generating an address requires more computational power than performing an SHA256d. A p2pkh requires you to perform ECDSA, SHA256, RIPEMD-160, SHA256 again, SHA256 again #2 and then just a base58 encoding.