Quote from: BurtW on December 28, 2015, 07:57:55 PM

Assuming my pattern assumption is correct then the underlying sequence was masked off to create the private keys.

Now if the underlying sequence before masking came from a cryptographically secure random number generator there is no hope of predicting the 51st private key and brute force or random chance in 51 bits is the only chance.

However if the underlying sequence was mathematically generated then maybe the keys are predictable.

Exactly.

I think the best is if we find a mathematical formula for the sequence (if it really exists).

For example, if you look at the decimal values, they seem to be always close to the double of the previous value, excluding the first few values.

Quote from: DannyHamilton on December 28, 2015, 08:03:06 PM

Quote from: unamis76 on December 28, 2015, 08:00:13 PM

So how were the results on the OP reached? Simply luck?

I'm pretty sure that the results that have been found by the OP so far were found with brute force attempting every value between 1 and 2²⁰.

The problem is that finding each subsequent result requires exponentially more attempts than the current result, so as the number of bits increases it becomes much, Much, MUCH more difficult to check the entire search space.

Exactly.

By the way, address 20:

KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYjgd9M7rHfuE2Tg4nJW
1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
pvk decimal value: 863317
pvk hex value: D2C55

So these are the decimal values we have:

Address 2: 3
Address 3: 7
Address 4: 8
Address 5: 21
Address 6: 49
Address 7: 76
Address 8: 224
Address 9: 467
Address 10: 514
Address 11: 1155
Address 12: 2683
Address 13: 5216
Address 14: 10544
Address 15: 26867
Address 16: 51510
Address 17: 95823
Address 18: 198669
Address 19: 357535
Address 20: 863317
Address 21: ?

Quote from: DannyHamilton on December 28, 2015, 08:00:24 PM

-snip-
If that is what's going on here, then there may not be a "formula" or "pattern" that can be used. To get the 51st address, you'd just have to brute force try all addresses associated with private keys between 1125899906842624 and 2251799813685248 (which is only about 1.126 X 10¹⁵ addresses).

Yes, that's a lot of brute force right there Grin