Distribution of nonces and hashes

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Here we analyze the nonce values and hashes for all the valid blocks in the blockchain:

Time Evolution[edit]

Nonces vs Hashes (y-axis logarithmic, x-axis linear)[edit]

This plot readily shows that the distribution of nonces that produce valid hashes is uniform.<br>

Nonces vs Hashes (log-log scale)[edit]

In the animated version of this last plot, you can really visualize the change in the difficulty and even see where the difficulty was decreased.


Distribution of Nonces[edit]

The nonces found are skewed toward 0 because this is a selection effect: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:<br>

Distribution of Hashes[edit]

Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>

2-D Distribution of Nonces & Hashes[edit]

2-D histogram of hashes and nonces (logarithmic color scale):<br> <br> This also illustrates very well that the distribution of nonces is uniform.



See Also on BitcoinWiki[edit]