# Proof of work: average number of tries to create a block

First, I'm sorry if I'm asking a stupid question. I'm just trying to understand bitcoin. I'm reading the Ethereum white paper, and I couldn't understand this sentence about proof of work:

At the current target of ~2^187, the network must make an average of ~2^69 tries before a valid block is found

My question: how the 2^69 number of tries is computed?

## Updated:

My question: why 2^69 instead of 2^70 or 2^169?

• Are you asking how to determine the number of tries required to solve a block given a difficulty target? Or are you asking what physical operations take place in order for a miner to "try" to solve a block? – KappaDev Oct 4 '18 at 1:36
• The 69 is just 256-187 because the hashes are 256 bits long – MeshCollider Oct 4 '18 at 4:51

As to why it is this way is just a function of probability. If you have a range of 1-100, and your target is `<= 20`, there are 20 numbers that satisfy your requirement. Thus, `20 * 1/100`, or 20 tries out of 100 should result in a valid number against your target.
It works the same way, although on a much larger scale here. Your target and attempt are both 256 bits numbers, which means they range from 0 to `2^256-1`. If your target is `2^179`, it means that `256-179`, or `2^67` tries will, on average, produce a valid number against the target.