The Ramanujan Machine

Yeah I’m not professional (I have a BSc in mathematics) and all this looks fairly introductory. Moreover there are lots of easy ways to calculate these constants like Pi (like taylor series) not even mentioning e can be easily calculated to whatever precision you need from its definition

The security properties of Proof of Work cryptocurrency are derived from the wastefulness. We want to be confident that everyone has the same cost when producing a block.

If the problems being solved are useful, they are potentially more useful to some parties than others, meaning some parties may have a lower cost to attack the blockchain, because it was computation they needed to spend money on anyway, might as well attack a blockchain while you are at it.

I can try to explain further if that's confusing.

A key component of the hash algorithm used by blockchain is that difficulty can be adjusted, such that the algorithm ensures that the difficulty to mine the next block increases/decreases based on how long it took previous blocks to mine. In this way the network can attempt to maintain a predictable rate of blocks being mined as mining power fluctuates.

So for this to be a good computation for a blockchain to use it would have to have a way to modify difficulty in a predictable way.