Quote from: mcdouglasx on Today at 04:47:08 PM

For those who don't understand prefixes, if you want to try your luck, this is the best current option for puzzle 71. If you're not interested in searching the entire range, where random + sequential and prefixes are equal in terms of statistical significance, you're just trying your luck, which means you don't need to scan the entire range. You get better results by using prefixes, which have huge advantages.

https://bitcointalk.org/index.php?topic=5546684

Sorry, but saying that prefix searching is "undoubtedly the best option" is simply not correct when you look at the math and real benchmarks.

Example:
If you have 100,000 hashes to check, both prefix and sequential search will, on average, require about 50,000 checks to find the target. This is what your own stats show:

Sequential: ~50,300 checks

Prefix: ~49,900 checks
The difference is less than 1%. All statistical tests made by academics (t-test, Mann-Whitney U) show no significant advantage, see your p-values (>0.3 or even 0.86).

Why?
Because unless you have a way to skip big chunks of the search space without missing the target, changing the order (prefix vs. sequential) doesn’t change the fundamental probability: you still have to look, on average, at half the dataset to find your answer (see Knuth, TAOCP Vol. 3, or any standard algorithm book).

Prefix filtering only helps if you’re not doing a full search, e.g. if you just want to try your luck in a small subset, but then it’s just a probabilistic guess, not an efficiency improvement.

Proof:

Knuth, The Art of Computer Programming, vol 3: Sorting and Searching https://www-cs-faculty.stanford.edu/~knuth/taocp.html

Prefix searching does NOT make brute-force key searches fundamentally faster. The numbers don’t lie.