Quote from: zebedee on April 22, 2015, 12:12:29 PM

Quote from: teukon on April 21, 2015, 04:22:51 AM

This is a thorny topic and really depends on what you mean by "usable" and "lost to accidents". Of the oft-cited 21 million BTC total:

some are at addresses for which it is not known that a corresponding private key exists (1111111111111111111114oLvT2; The Bitcoin Eater address;

I guarantee you trillions of private keys corresponding to that address exist. Mathematically around 2^96 should exist by the pigeon-hole principle. So the probability that none do is so crushingly humungously vanishingly small that it makes creating a SHA256 preimage look like child's play.

It is true that there are approximately 2⁹⁶ distinct private keys per address on average but I don't know how much can be said about the "lumpiness" of the distribution at this scale. It seems plausible to me that something subtle in the algorithm causes some addresses to have many more than the average number of solutions while others have far fewer. I don't see why there cannot be gaps of unobtainability scattered throughout the distribution, gaps too narrow to be discovered even with extensive testing.

If the distribution is seemingly random and uniform at the scale of individual addresses then I completely agree with your assessment of the probabilities. Indeed, I would go further and claim that RIPEMD-160 is likely surjective.