Proof of Work – Is it always possible to find a hash that starts with a certain number of zeros?

The core principle of hash functions like SHA-256 is that for a given input, they produce a seemingly random output, and that the output is uniformly distributed over the possible range. This means that for a given input, there is about a 50% chance that a particular bit will be either a 0 or a 1. So the probability that the first bit is 0 is 1/2, the probability that the first two bits are 0 is 1/4, the probability that the first three bits are 0 is 1/8, and so on.

These properties make it almost statistically certain that there exists a valid input that produces a hash with a certain number of leading zeros. All you have to do is try enough inputs (or “nonces” for ₿ mining) until you find it. This is what ₿ miners do in a proof-of-work system. They try billions of different inputs every second until they find one that produces a hash with the required number of leading zeros.

What if there is no such number?

₿ The network cannot create new blocks matching the current difficulty level.