Is it true that the "seed words" bruteforce more reliable for to get profit than searching of a "random number" for to open some profitable outputs?
The last one is impossible due to math, but the first one?
Bitcoin Stack Exchange is a question and answer site for Bitcoin crypto-currency enthusiasts. It only takes a minute to sign up.Sign up to join this community
No, it is not true. Both are impossible due to math. The mnemonic is just an encoding of a number that is randomly generated (i.e. just like a private key) so it has the same security properties of that 256-bit number.
If you ignore that it encodes a number, consider this: a seed phrase encoding a 256-bit number needs 24 words in the mnemonic. There are 2048 possible words which means that there are
2048^24 = 2.964... × 10^79 possible mnemonics. There are
2^256 = 1.157... × 10^77 possible 256-bit numbers. There are actually more possible mnemonics than there are values to be encoded in the mnemonic. Thus the mnemonics are just as secure as a randomly generated private key (256-bit number) itself.
See also this article about Deterministic Cryptocurrency wallets: https://en.wikipedia.org/wiki/Cryptocurrency_wallet#Deterministic_wallet and BIP39 Mnemonic code or sentences on: https://en.wikipedia.org/wiki/Bitcoin_Core#Bitcoin_Improvement_Proposals