Combinatorics of Bitcoin mining: *difficulty* vs number of trials of nonces and $32$ bit nonces
According to this question Mining Difficulty and Leading Zeros the Bitcoin mining problem is to find a string s = (hash of previous block + Merkle Tree Hash + nonce).
The current difficulty is roughly to find a small hash which has $19$ or $20$ leading zeros in Hexadecimal.
- $16^{20}=2^{80}$ which is a huge number and a random number hashed out has a probability $\leq\frac1{2^{80}}$ to have $80$ leading $0$ binary digits.
This number is much larger than trillions or quadrillions.
However the quoted difficulty of hashing to find leading $19$ or $20$ Hexadecimal digit $0$s is in order of $100$s of trillions.
a. Shouldn't the difficulty be roughly $2^{80}$ tries?
b. Why is the difficultynumber smaller?
c. How does the difficulty number related to number of random tries which is roughly $2^{80}$ in the case of $20$ leading zeros?
- How large in number of bits is the nonce? Isn't it $32$ bits? Is it bigger than $80$ bits? If not how can we try $2^{80}$ possible nonces given that hash of previous block + Merkle Tree Hash is a fixed value and only nonce change determines the changes in the computed hash?
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