I have managed to lose 5 words of my 24 word Ledger Nano S recovery phrase. I have words 1-19 but I am missing words 20-24.
I have significant holdings on the wallet so would very much like to recover it if possible.
The passphrase is a BIP39 mnemonic (see https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki).
I have the bitcoin and ethereum public addresses for this mnemonic. I am wondering if it’s feasible to brute force the passphrase.

Each word is 11 bits (2^11 = 2048 possible words).
The last (24th) word of the passphrase is of the following form [3 random bits][8 bit checksum].
Therefore I only have to check 2^(55 – 8) = 2^47 = 1.4×10^14 combinations.
I would have to compute SHA-512-HMAC with an iteration count of 2048.
As far as I understand, that means I’d have to compute 1.4*10^14 * 2048 = 2.87*10^17 hashes in total.

Is there any hardware out there designed for this? I am aware of ASICs that compute sha-256 hashes but not sha-512 hashes.
Perhaps I could tweak one to work with sha-512 since they are very similar.

Assuming a fairly typical ASIC hashrate of 1TH/s (10^12 hashes per second), I could exhaust the search space in 2.87*10^5 = 287000 seconds = 3.3 days. I’d probably get there sooner, of course (expected 1.65 days). Time is not something I am worried about. Even if I have to wait months, I don’t mind – so if I can get 10GH/s at a reasonable price, that would be great.

I would really appreciate any help/information you could provide to help me out and make sure I haven’t missed anything.
I could also use GPUs for this (I calculate I can run them at roughly $1/10TH – so it would cost me $28.7k to exhaust the search space, which I will do if there are no cheaper options).

Many thanks,
James

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By pplny

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