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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
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    The 69 is just 256-187 because the hashes are 256 bits long – MeshCollider Oct 4 '18 at 4:51
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As MeshCollider's comment mentions, it is simply the difference between the total number of bits against the target bits.

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.

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