I got interested in the research that Sergio Demian Lerner did on early Bitcoin blocks. It is widely known as the Patoshi pattern. His argument about Satoshi running a miner from the very beginning seems logical to me and his findings are in fact showing it. But his second finding about the anomaly in the Least-Significant-Byte (LSB) of the nonce field of block headers really got my attention.

Histogram of LSB Byte of the nonce field (by Sergio Demian Lerner)

Sergio points out in his blog post, that this histogram was created from the data of genesis block up to block 36,288. As you can see, nonce LSB values are not uniformly distributed in terms of frequency, and clearly some values have much higher frequency than others. Values 0 to 9 and 19 to 58. Apparently, this finding has shown some correlations with the famous Patoshi pattern, but I’m not going to discuss them here.

The first thing that caught my eye in this chart, was that the frequency of these values are different from each other. For example, the frequency of values 20 to 28 is much higher than others. So I tried to figure out this mystery by regenerating this histogram with a wider block height range. This is what I got for the first 60,000 blocks:

We see a slight increase in the frequency which is expected because we have added more data to the calculations. But the shape and pattern seems the same as the previous chart. This time, I decided to make the range narrower. For the first 10,000 blocks I got this:

Interestingly, we see that the frequency of LSB values between 20 and 28 has decreased in comparison to other values and they haven’t peaked like before. After trying some other block height ranges, I decided to observe the histogram through the time so that any change in the shape of the histogram would pop out.

Here is what you get if you draw the histograms of a moving window of 3,000 blocks for the first 60,000 blocks:

We are observing that there exist five different ranges of LSB values based on their behavior in the histogram:

  • [0–9] has peaked from the first block to around block 54,000. It goes for a dip at around block 21,000 and peaks back at 24,000

At this point I started searching for similar findings just to see if anyone has explanations for what I’m seeing and found out that OrganofCorti has already observed changes in the hash rate and LSB value restrictions before, which perfectly matches with my observations.

So 5 ranges, each have 10 numbers in them, except for the second range, [20–28], which has 9 numbers. At first I had the number 19 in the second range, so all ranges had 10 numbers in them. But something is different about this particular LSB value. It behaves really like the second range, but for some unknown reason it’s frequency is almost always half of the others. This is what I’m observing:

So maybe this weird behavior of LSB value of 19 is telling me to start looking at this whole thing in a different way. Or maybe not.

I would love to hear all your thoughts about this.

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