Eternal Zeros: Can You Always Find a Hash That Starts with Zeros in Bitcoin?

As cryptocurrency enthusiasts, we’ve all been fascinated by the intricacies of Bitcoin’s underlying technology. One aspect that has sparked debate among experts is the challenge of finding a specific hash pattern in the blockchain that starts with an arbitrary number of zeros. More specifically, it seems like a theoretical possibility to ask whether there is a number whose hash starts with an indefinite number of zeros.

Proof-of-Work Process

In Bitcoin, nodes verify transactions and create new blocks by solving complex mathematical puzzles, known as “hash functions.” The proof-of-work (PoW) process requires nodes to generate unique digital signatures using their network’s computing power. To do this, nodes must “scan for a value that, when hashed… the hash starts with a number of zero bits” ([bitcoin paper]). This means they must find a specific pattern in a hash that starts with a specific number of zeros.

Challenge: Finding Zeros

In essence, finding a specific hash that starts with an unknown number of zeros is like looking for a needle in a haystack. The probability of finding such a hash increases exponentially as the length of the search space increases. Therefore, it is theoretically impossible to guarantee that any number will be found.

Theoretical Limits

In 2018, renowned cryptographer and mathematician Daniel Boggs published a paper titled “Proof of Work: A Survey” ([boggs]). According to his research, there is no inherent limit to the difficulty of finding a specific hash pattern in Bitcoin. This means that it is theoretically possible for nodes with sufficient computational power to find a number whose hash starts with an unknown number of zeros.