Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it
You should straight up go to Princeton and give some lectures about this before they call the police.
Finding more than 1 (a prefix of length 3) in 4096 is rare, and omitting the target is even rarer. The length of the prefix doesn't matter as long as the block matches what's expected.
Nor do you try as much as you try, the probability will remain ≈ the same.
If finding more identical prefixes within 4096 were no longer so rare, the hashes would be broken.
I will again state that you don't really understand how an uniform distribution works. You're simplifying to a yes/no gambling, forgetting completely about the basics of it.
If finding more prefixes in some portion means the hash's broken, man, please don't make me provide actual examples about how wrong you are.
When you skip some rest of "block" as you call it, you simply move off the chances of finding (or not finding) another prefix, into the next block. Basically, a futile operation to perform, because it goes the other way around too: when you fail to find some prefix in the next "block" or whatever, it might simply mean (at an average level) that it was found in the skipped portion. Or any other portion, anywhere, to be honest. Because, for the 9000th time (for you): it's an uniform distribution, all keys are as likely as others, and all ranges are as likely as any other ranges.
So you're simply selling some illusion of some sort of benefit, but it does not exist, neither in theory, nor in practice. It would be great if it would, though.
The advantage of prefixes is that it's not common to find multiple prefixes of a hash in a space x where their probability is 1/x. This math isn't going to change even if you cry. For that single, indisputable mathematical reason, searching with prefixes is the most convenient, since they're based on REAL probabilities, the properties of a uniform distribution.
1st grade fact: A uniform distribution only means that the target is equally distributed, not that all stopping criteria perform equally.
LOL, each stopping criterion changes the probability of success within the block, even with a uniform distribution.
Pruning by 3 hex prefix: success ≈ 63.2%
Stopping at a random point: success ≈ 50%
Finding ≥ 2 prefix collisions in 4096 keys is very rare; if it were frequent, the hash function would be compromised (this doesn't mean there can't be cases where it happens, but the point is that for what the prefix lookup requires, it works).
Missing the target due to premature collision occurs in the remaining ~36.8%, just as the script predicts. I don't understand why you flatly deny this fact.
Instead of continuing to cry or hesitate, accept it.
I'm 100% sure you understand what I mean; your time, like the modern Digaran, is simply imprinted on you.
snip
Come on, man, you're taking all the fun out of mixing so much nonsense into a single post.
The 3-hex filter is 1/4096 in any space. It doesn't matter if the hash has 40 digits, the probability of matching the first 3 is always the same.
Limiting the range doesn't "fix" the math: the uniformity remains within that subspace, and the formula applies the same.
Going from 4096 to 2**256 only changes the scale. The exponential form is the same; the relative result remains the same.
kgtimes, you won't respond to this guy's statements, or you'll apply the "the enemies of my enemies are my friends" rule
.Buddy, here’s the A + B you keep dodging:
A. Toy range vs. real world
Your demo space = 2¹⁷ ≈ 131 k keys.
Hit rate for a 3-hex prefix there: (131 072 / 4096) ≈ 32 possible matches — easy pickings.
B. Actual Bitcoin key space
Size = 2²⁵⁶ ≈ 1.16 × 10⁷⁷.
Same prefix filter: 2²⁵⁶ / 4096 = 2²⁴⁴ ≈ 2.9 × 10⁷³ candidates.
At 1 trillion keys/sec (fantasy hardware) you’d still need ≈ 9 × 10⁶¹ years to exhaust those 2.9 × 10⁷³ keys. Your “67% success” collapses to 0 % in any universe that isn’t a 131 k fishbowl.
Uniformity doesn’t save you; it condemns you: every prefix is evenly packed with an astronomical number of keys. All you did was shrink the pond, hook a fish, then brag you’ve solved deep-sea fishing.
Keep moving those goalposts, mathematics will keep flattening them.