What does the difficulty number mean?

[t1mm3h]

I used the search function but didn't find an answer.

I did read about difficulty on https://en.bitcoin.it/wiki/Difficulty, but the number still doesn't make sense to me. Can anyone explain me what this number means and how to use it?

[theymos]

It means that the difficulty of mining a block is 11,187,257 times harder than it was when Bitcoin was first created.

[DeathAndTaxes]

It is an arbitrary number.  The network began at difficulty 1 which requires on average 2^32 attempted hashes to solve a block.  

Difficulty 11 million is simply 11 million times more difficult than difficulty 1.  In terms of hashes it currently takes on average 2^32 * 11,187,257 =  48,048,902,946,947,100 (~48 quadrillion) hashes to solve a block.

[t1mm3h]

It is an arbitrary number.  The network began at difficulty 1 which requires on average 2^32 attempted hashes to solve a block.  

Difficulty 11 million is simply 11 million times more difficult than difficulty 1 (i.e. currently it takes 2^32 * 11,187,257 hashes on average to solve a block).

Thank you, makes sense! Why did it take 2^32 attempts with difficulty 1? I know Bitcoin works with a target hash and SHA-256. There must be a (complete) way to calculate the average number of hashes required with a certain target. Anyone can help me with this?

[DeathAndTaxes]

Once again the choice of 2^32 was arbitrary.  The block header has a 32 bit nonce and given computing power available at the time (unoptimized CPU mining) difficulty 1 was acheiveable by roughly a dozen or so nodes so it seems that likely factored into the starting difficulty.  Bitcoin could work just as well if the difficulty was 48 quadrillion, initial difficulty was 4 billion and difficulty directly represented the number of hashes required.   It is a completely arbitrary number really only useful in comparing changes in difficulty.  If I can mine ~1 BTC per day on existing hardware and difficulty doubles I can expect to only mine ~0.5 BTC per day.  If difficulty fell 90% I would be able to mine 10 BTC on the same hardware.

BTW:  I really wish that regardless of how difficulty was computed, that Satoshi had used a 64 bit nonce value in the block header.  It would have greatly simplified the mining protocol.  Maybe simplified isn't the right would but it would have been more elegant than the nonce + extranonce (in coinbase) "hack".

[Bitoy]

Very informative.  Thanks for the answer