If anyone wants to try to analyze the bit patterns of the already solved puzzles to make a more "direct" (for lack of a better word) search algorithm that doesn't just spray everything like bruteforce, here are the first 65 private keys in binary form:
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So don't waste your time by looking for deterministic wallet patterns, or comparing the solved keys with unsolved keys as I said and Satoshi himself said it, there is no pattern, not because we don't want people to solve them, but because we don't want them to waste their time.
There may not be a pattern, but that doesn't mean we should not use a probability-based analysis of the keys. For example, analyzing the last bit of these keys gives the information that even keys occur SLIGHTLY more than odd keys, but the difference is a bit more pronounced when taking only the bottom half of this sample (i.e. keys #33 to #65). But the more useful information can be gleaned by looking at heuristics, not at single bits.
In any case, here are the statistical sample of each keys that have a sequence of two or more "1" bits:
- 2 consecutive ones: 61/65
- 3 consecutive ones: 51/65
- 4 consecutive ones: 33/65
- 5 consecutive ones: 21/65
- 6 consecutive ones: 10/65
- 7 consecutive ones: 2/65
- 8 or more: negligible (the highest is puzzle #56 with 10 consecutive ones).
What this means is, all the paths that have 7 or more ones can basically be discarded, making for a much faster brute force. I could do a similar analysis for zeroes, but I need to remove the leading zeroes first to avoid skewing the data.
And also:
94% chance of having at least 2 (key word here is AT LEAST) sequential ones (i.e.
you can get rid of 01010101010 and so on)
78% chance of 3 or more seq. ones
51% chance of 4 or more seq. ones
32% chance of 5 or more seq. ones
15% chance of 6 or more seq. ones
Apparently, the longer you make the sequence, the probability drops by one sixth. So anyone who has done some sports betting before should have a good gauge at the odds here and what should be the threshold.
