Why does the Genesis block appear to have a lower hash than necessary?

Question

The hash of the genesis block of bitcoin has two extra 0 as compared to other block hashes. According to the logic, it should have been the same as they all have the same difficulty. Why is it so? Was any special reason for doing so?

Hash of genesis block : 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f

Hash of block 1 : 00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048

Hash of block 2 : 000000006a625f06636b8bb6ac7b960a8d03705d1ace08b1a19da3fdcc99ddbd

Answer 1

The SHA256 hash algorithm produces what looks exactly like a random number in the range 0 to 2²⁵⁶-1 (1.1579208923731619542357098500869e+77). Each of those values should be equally likely.

So if you produce a large number of these by altering the data to be hashed, you cannot steer the results and most of the results will be a large number.

Some of the results will be a small number and a few will be very small. It is perfectly possible that the first result that is small is also very small - there is nothing impossible or surprising about that.

Since the genesis block had no history, there should be no expectation that the target value was especially precisely calculated to match the exact hashing power available.

Furthermore, I would expect the target would have been high (low difficulty) since there were very few miners (only one?) - The higher the target, the more space there is for a solution to be some orders of magnitude smaller than necessary. If conversely the difficulty was so high that hashes had to be less than 42, there would be no room for a successful hash to be two orders of magnitude smaller than needed.

Answer 2

Bitcoin difficulty is not determined by the "number of zeros", but none the less the Bitcoin genesis block would satisfy a difficulty target substantially higher than might be expected. This doesn't really mean anything in the scheme of how the system operates, it's just a curiosity.