Bitcoin hash rates/difficulty

Difficulty is defined relatively: it is how much more difficult it is to mine a block compared to a fixed "maximum target", which corresponds to roughly 2³² hashes.

In more detail, a Bitcoin block is PoW-valid when its hash (interpreted as a 256-bit integer) is less or equal to that block's "target". Difficulty does not exist at the protocol level; internally, everything uses targets.

The rules for target adjustment are as follows:

• Blocks whose height n is not a multiple of 2016 have the same target as their parent block.
• Blocks whose height n is a multiple of 2016:
  • Take the parent's target
  • Multiply that target by the number of seconds in two weeks.
  • Divide the result by the difference (in seconds) between the timestamp of block n-2016 and that of block n-1.
  • If the result is more than 4 times the parent target, or less than 1/4th of the parent target, clamp it.
  • If the result is above the maximum target, use the maximum target instead.
  • Round the target down to fit in Bitcoin's custom 32-bit floating point format (called the "nBits" encoding).

The expected number of hashes at a given target T is 2²⁵⁶ / (T+1). The higher the target, the easier it is to mine a block. The maximum target is thus a limit on how easy mining can get, and is the fixed constant (2²²⁴ - 2²⁰⁸) in Bitcoin. The expected number of hashes at this target is 2⁴⁸ / (2¹⁶-1), or just over 2³².

The difficulty is now a purely human representation of the target value: it is the maximum target divided by the actual target, and is at least 1 (at maximum target).

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