All 4 nounces very close by.
Not close at all. A difference 300,000 is about one thirteenth of the maximum range, which means consecutive nonces will be this close together over 10 times a day.
4Byte nounce is between 1 and 2^32-1=4.294.967.295 right? Where is your 300.000 being 1/13th coming from?
I meant 300,000,000 (that's the closeness we're talking about right?), but I misplaced a few zeros somewhere around the second glass of absinthe. This is why you shouldn't drink and derive.
Be careful with absynthe...
Let's look closer at nounces:
We assume that nounces are uniformly distributed (not exactly true since if we start increasingly with nounce 0 they follow a Poisson law, but taking into account that nounce cycles many times before finding the solution it is well approximated by the uniform distribution). We look at distance mod 2^32.
|nounce(354641)-nounce(354640)| = 19.452.599 probability 19.452.599/(2^32-1)*2 = 1.8%
|nounce(354642)-nounce(354641)| = 5.394.922 probability 5.394.922/(2^32-1)*2 = 0.12%
|nounce(354642)-nounce(354641)| = 313.864.936 probability 313.864.936/(2^32-1)*2 =7.2%
Combined probability 0.000155% that is 1 in 64.5 million of times.
Are you trolling? 0.000155% is 1 in 645161
And this is nonsense. Just some made up data
|nounce(1)-nounce(0)| = 5%
|nounce(2)-nounce(1)| = 20%
|nounce(3)-nounce(2)| = 10%
|nounce(4)-nounce(3)| = 1%
|nounce(5)-nounce(4)| = 5%
|nounce(6)-nounce(5)| = 10%
Combined probability 0.000005% that is 1 in 20 million of times. Bitcoin in broken!!!
I just did a rough approximation, only valid for small probabilities and few events. You are welcome to do the exact computation.
You calculate in a wrong way. You should define the meaning of "close"
a priori. That could be 20%, 10%, or 1%.
Let say you choose 10%, the P(1.8%, 0.12%, 7.2%) should be 1/1000, not 1/645161.
And let say you choose 2%, the P(1.8%, 0.12%, 7.2%) should be 1/2551 (0.02*0.02*0.98). Therefore, one event of this kind is expected in about 2 weeks.
Please stop here (and edit your misleading topic) unless you find something really statistical significantly deviated from the theoretical distribution.
I don't understand what you mean.
OK, let me do the computation and explain things carefully. You can tell me on which point you disagree.
(0) Put your 2^32-1 integer values on a circle of perimeter 2. This geometrical representation will help you.
(1) We assume uniform distribution of nounces. This is correct as first approximation, but not totally accurate as pointed out before by several people. We may extract the historical distribution and use it.
(2) The probability that two consecutive nounces are closer as nounce(354641) and nounce(354640) is 1.8%. It is the minor arc length between the two nounces on the circle.
Same for nounce(354642) and nounce(354641), and for nounce(354643) and nounce(354644). Otherwise, please correct me if you disagree.
(3) We assume independence of nounces with respect to previous nounces, i.e. we consider nounces as independent random variables.
This implies that distance between nounce(n+2) and nounce(n+1) is independent of the distance between nounce(n+1) and nounce(n).
(4) Thus, the probability of having three consecutive events of the sort described is just the product of the probabilities, it is 1 over 645161.
The probability of seeing this is on average once each 12.27 years at an average production of one block (nounce) every 10 minutes.
My conclusion is that the nounces produced by this miner are likely not independent and the mining procedure is not the usual one and it uses previous block computations or doesn't uses much the nounce variable.
But this is just one piece of evidence.
The second one, about the block size, also points to the fact that it is the same miner who mined the blocks. 731 kB blocks are quite common as noted earlier by someone else, but it is not
very likely either to find them consecutively. Moreover I bet that they cluster more often than expected and this can be checked running statistics on the blockchain.
The third piece of evidence is how close in time are these blocks. THe probability is not alarmingly small and can be computed by the Poisson distribution that follow times between blocks.
The fourth piece of evidence is the non-chronological timestamps that suggest that the timestap maleability is also used as nounce (this fact was already noted for blocks with only one transaction).
The fifth piece of evidence is that the first block is mined by AntPool and the next 3 by anonymous. It is not so common to have consecutive anonymous blocks,
This indicates that the miner is trying to hide that he is the same one mining.
All this "coincidences" are extremely unlikely and point that something is going on there.
