Facebook have so far secured 350,000 of the latest Nvidia H100 GPUs to power their AI efforts. (H100s cost roughly $30k each, so no small investment).

They are hoping it will be enough power to create the world's first AGI, but is it enough to crack a Bitcoin key by brute force, I wondered - so I ran the Maths (or 'Math' if you're American).

If you could gain access to Satoshi Nakamoto's dormant Bitcoin account by guessing his key, you would find a treasure trove of ~1m Bitcoin, which at today's prices would make you the world's 25th richest person at roughly $56bn.

Let's look at the figures: We need to know two main things:

• The Bitcoin Private Key Space: Bitcoin private keys are 256-bit numbers, leading to a possible 2²⁵⁶ different combinations.
• Hashing Speed of an H100 GPU: the speed at which an NVidia H100 can attempt to guess the key, measured in hashes per second (H/s).

NVidia H100 GPUs, incredible as they are, were not designed to smash out SHA256 hashes as efficiently as a Bitcoin ASIC (Application-Specific Integrated Circuit) but they are still brutally powerful and have been estimated with a hash rate of up to 900 MHs - that's ~900,000,000 attempts to crack the key every second.

That gives:

• Total combinations to attempt: 2²⁵⁶
• GPU speed of an H100: 900 MH/s (900,000,000 H/s)

Working at this speed, 350,000 NVIDIA H100 GPUs with a hash rate of 900 MH/s would still take approximately 1.17 × 10 ⁵⁵ years to brute force Satoshi Nakamoto's Bitcoin private key.

This is longer than the age of the universe (13.8 billion years).

Quite considerably longer in fact, by a factor of 44.

It is mind-blowing just how many possibilities there are to rearrange only 256bits of information, making the time required to guess a key unfathomably large. This exercise underscores the practical impossibility of brute-forcing Bitcoin private keys with any current or near-future (non-quantum) technology.