Quote from: rapazev on May 15, 2016, 11:26:27 PM

Quote from: shorena on May 15, 2016, 08:30:01 PM

Its impossible.

Not impossible, just highly improbable Grin

-snip-

Do you worry about the air in your room spontainously moving into a corner leading to your suffocation? Its the same realm of "improbable". Calling it improbable will give people the wrong impression.

Quote from: cyberguy on May 16, 2016, 06:20:39 AM

Quote from: ebyccc on May 15, 2016, 07:38:10 AM

I am quite new to bitcoin, still reading the guide, and being puzzled about this. For example, if somebody just create one million private keys and run one million wallet programs at the same time, he would much likely receive some output that paid to one or more private keys (addresses maybe) he generated, and thus steals others' money
Could this be a problem?

A private key is a 256 bit binary number. When written in hexadecimal this comes to a 64-digit hexadecimal number, which in decimal is approximately 1.158 x 10^77. Each private key will produce a unique public key and corresponding bitcoin address. So there are 2^256 possible combinations of private key, public keys and bitcoin addresses.

No, due to the use of RIPEMD160 there are only 2¹⁶⁰ possible bitcoin addresses (of version 1).

Quote from: cyberguy on May 16, 2016, 06:20:39 AM

To get an idea of the numbers we are dealing with consider the following.

The world's fastest super computer is currently capable of performaing 33.6 quadrillion (33.6 x 10^15) calculations per second. Even if we assume that this makes it possible to check one private key per calculation (the actual number will be less since checking whether a particular private key agrees with a given bitcoin address will need much more than one calcultion), it would need 3.45 x 10^60 seconds or 1.1 x 10^53 years to try all possible private keys. So to try and steal bitcoins that are at a particular address by trying all possible addresses, though theoritically possible is computationally infeasible.