Exploring Key Factorization Strategies

Anyone tried looking at the BTC Puzzle? I think we should simplify it using a probabilistic approach. Like, if we analyze the keys we've found, most aren’t even prime.

So, if I'm getting this right, since at least one key in a set of 10 likely has factors in every lower bit range, we might be able to narrow down the problem. By carefully selecting the bit ranges, we could reduce brute-force options while speeding up the process.

Hey all, I gave puzzle 64 a shot. Since I know the private key, I used some sites to get its factors and tested it. But none of my strides worked. I even subtracted 1 due to the starting key. What did I do wrong?

Have you thought about converting those strides to hex? Maybe considering them as decimal isn’t the best way.

Finding prime numbers is tricky. When you only compute non-primes, you still have tons of numbers in Z(2^256) that are non-prime. You could be multiplying by various factors, but without a better method, it’s just tedious. Plus, if you search in a specific order, you might miss the key.

I did convert to Hex and subtracted 1, but I still feel lost. I need more time to test this properly.

What do you mean by "all possible factors"? I’m curious about how you found that pattern you showed in your graphics.

For puzzle 65, I generated 400 random private keys between puzzles 64 and 65. The pattern you mentioned appears about 1 in 10 times, so I doubt this is a reliable shortcut to finding private keys.

It’s not about how the keys are generated, we know that part. The key is to figure out the most relevant range first, especially with 84 puzzles left to solve.

How do these factors relate to the number of 0s and 1s in the private key in binary? Like, if the number of zeros minus the number of ones is 6, does that make it more likely to be a key?

By the way, puzzle 66 had some interesting stuff too.

+1, definitely more to explore here.