Quote from: MrFreeDragon on October 16, 2019, 01:26:22 PM

bounty0z, there was no some pattern. All the keys were random.
However, i made some analysis of all the private keys for the "opened" wallets, and can say that more likely the key has the following property:

Quantity on bit "1" in the key is 45%-55% from the total bit quantity

This means that for the wallet #64 the total quantity of "1"s in the key is from 29 to 35 with the leading first bit "1" (first bit is always "1" for all keys in the puzzle). To increase your chances youl should take 29-35 "1"s, randomly mix them with the remaining "0"s and you will receieve the key. The key consists from let's say 10 "1"s bit and 54 "0"s bit is not the key for #64, as here only 15% are "1"s and the majority are "0"s.

How did I receieve this? I had a look at all the private keys in BIN format, and found that the average quantity of "1" in all the keys is 51%, the total range is 40-60%, but the most likely is 45-55%. Please have a look at all the known private keys in BIN formmat and the calculation of "1"s and "0"s in them.

Code:

No. K%rng 1's 0's %1's Private Key in BIN
01 100,00% 1 0 100% 1
02 100,00% 2 0 100% 11
03 100,00% 3 0 100% 111
04 0,00% 1 3 25% 1000
05 40,00% 3 2 60% 10101
06 58,06% 3 3 50% 110001
07 20,63% 3 4 43% 1001100
08 76,38% 3 5 38% 11100000
09 83,14% 6 3 67% 111010011
10 0,59% 2 8 20% 1000000010
11 12,90% 4 7 36% 10010000011
12 31,07% 8 4 67% 101001111011
13 27,37% 4 9 31% 1010001100000
14 28,73% 5 9 36% 10100100110000
15 63,99% 9 6 60% 110100011110011
16 57,20% 8 8 50% 1100100100110110
17 46,22% 11 6 65% 10111011001001111
18 51,57% 6 12 33% 110000100000001101
19 36,39% 12 7 63% 1010111010010011111
20 64,66% 10 10 50% 11010010110001010101
21 72,78% 11 10 52% 110111010010100110100
22 43,41% 12 10 55% 1011011110010000001111
23 33,49% 12 11 52% 10101010110111001010010
24 72,00% 9 15 38% 110111000010101000000100
25 97,80% 17 8 68% 1111110100101111011100101
26 62,54% 11 15 42% 11010000000011001001101110
27 66,82% 14 13 52% 110101011000011100001110101
28 69,60% 14 14 50% 1101100100010110110011101000
29 49,28% 16 13 55% 10111111000100101010100011110
30 92,44% 16 14 53% 111101100101001100110101100100
31 95,80% 21 10 68% 1111101010011111110011101000111
32 44,05% 15 17 47% 10111000011000101010011000101110
33 66,18% 16 17 48% 110101001011011001010100011011000
34 64,53% 16 18 47% 1101001010011001011001000100011101
35 17,07% 15 20 43% 10010101110110100100001000101110000
36 23,36% 17 19 47% 100111011110100000100000101001111100
37 45,89% 22 15 59% 1011101010111011101010110101010010011
38 6,94% 17 21 45% 10001000111000001011111010110011010000
39 17,77% 20 19 51% 100101101011111100000110000001111101001
40 82,56% 22 18 55% 1110100110101110010010010011001111010110
41 32,63% 21 20 51% 10101001110000110100110101100110001011011
42 31,67% 19 23 45% 101010001000100001110001011000110110001111
43 68,48% 24 19 56% 1101011110100111011001001111100010110010001
44 75,13% 22 22 50% 11100000001010110011010110100011010110001111
45 13,67% 19 26 42% 100100010111111001010000101000011110000000101
46 46,11% 19 27 41% 1011101100000110000011100010001101010101000100
47 70,06% 24 23 51% 11011001101011000010000101101010011110010111010
48 35,86% 31 17 65% 101011011110011011010111110011100011101110011011
49 45,35% 25 24 51% 1011101000001011101101011000000010101111101001101
50 8,56% 24 26 48% 10001010111101010000111100001011101001001101010100
51 82,86% 19 32 37% 111010100000111000010100001101000000000100111010100
52 87,25% 30 22 58% 1110111110101110000101100100110010111001111000111100
53 50,18% 24 29 45% 11000000001111000100011100100011111100011001001101100
54 10,74% 32 22 59% 100011011011111011011011010101101011010001111101000011
55 66,79% 31 24 56% 1101010101111100001111110011011011001111110000100010100
56 22,73% 34 22 61% 10011101000110001011011000111010110001001111111111011111
57 91,85% 29 28 51% 111101011001001011100100100000111100101011101011000011100
58 38,76% 25 33 43% 1011000110011101011011100001010010000110001001101000100001
59 82,17% 33 26 56% 11101001001011011001011101110000111110010101011010001001111
60 96,89% 32 28 53% 111111000000011110100001100000100101001101100111101110111110
61 23,67% 29 32 48% 1001111001001011010100011011101000010111101100100100100000110
62 69,49% 34 28 55% 11011000111101010101000001111010110110000100011010101111101110
63 95,01% 36 27 57% 111110011001110010111101111110110101100110011110110100000001000
65 65,71% 29 36 45% 11010100000111000101100010011010100000101101100100110100001100111
70 64,40% 34 36 49% 1101001001101110000100101101100100001100011010011011000100111011110001
75 19,32% 33 42 44% 100110001011100111000010001010001101000011010100001001100110110111000000111
80 82,89% 37 43 46% 11101010000110100101110001100110110111001100000100011011010110101101000110000000
85 9,03% 39 46 46% 1000101110010000011000100111100000001100011010101000110111000110011101011101110101000
90 40,23% 43 47 48% 101100111000000000101110110010000100110110101001000100010111000111000111101000010110111111
95 28,87% 48 47 51% 10100100111101001111001001010110001100000111100011111110110010010100000111010001011000111110100
100 36,98% 53 47 53% 1010111101010101111111000101100111000011001101011100100011101100011001111110110100100100100000100110

AVG 53% 51% Average for wallets > #15

Keep in mind that the fist 15 keys are not representative due to small length, so the average is calcualted for wallets greater #15.
Additional analytics for information purposes (i did not find any patterns here): K%rng is the actual private key range point (in %%). It means where the actual private key was found in the context of total range (0% is the 1st point of the range, 100% is the last point of the range). K%rng for wallet #n is (PrivKey(n) - 2^(n-1)) / 2^(n-1) * 100%

And what is the difference between the probability of setting a bit to 0 from 1? The probability is the same.
In this regard, the central reference point should be 50%. And the range should evenly expand into the wallpaper side. That is, 49-51, 48-52, 49-53, etc.

Quote

Quantity on bit "1" in the key is 45%-55% from the total bit quantity

Why is 45% -55%? If you take the data from the table excluding the first ten keys. Then we get a minimum value of 31% and a maximum of 68%. The difference is from 50%, 19 and 18, respectively. We take the maximum 19, 50-19 = 31, 50 + 19 = 69. That is, the search difference will be in the range of 31% -69% of the bits set to 1 or 0.

Well, in general, the right thought.

I already wrote above. You can also calculate the maximum duration of the same bits. And also use this parameter in the calculations.

By the way, the same algorithm with keys in hexadecimal representation.